LMFDB - Embedded newform 21.7.f.b.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,7,Mod(10,21)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("21.10");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	21.f (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.83113575602$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} - 787x^{5} + 38792x^{4} - 92833x^{3} + 1563109x^{2} + 3107772x + 38787984 $ x^8 - x^7 + 212x^6 - 787x^5 + 38792x^4 - 92833x^3 + 1563109x^2 + 3107772x + 38787984
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.1
Root			$5.73828 + 9.93899i$ of defining polynomial
Character	$\chi$	$=$	21.10
Dual form			21.7.f.b.19.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.23828 - 10.8050i) q^{2} +(13.5000 + 7.79423i) q^{3} +(-45.8323 + 79.3839i) q^{4} +(-175.367 + 101.248i) q^{5} -194.490i q^{6} +(284.280 + 191.921i) q^{7} +345.159 q^{8} +(121.500 + 210.444i) q^{9} +O(q^{10})$	\(q+(-6.23828 - 10.8050i) q^{2} +(13.5000 + 7.79423i) q^{3} +(-45.8323 + 79.3839i) q^{4} +(-175.367 + 101.248i) q^{5} -194.490i q^{6} +(284.280 + 191.921i) q^{7} +345.159 q^{8} +(121.500 + 210.444i) q^{9} +(2187.98 + 1263.23i) q^{10} +(-437.884 + 758.438i) q^{11} +(-1237.47 + 714.455i) q^{12} -275.049i q^{13} +(300.287 - 4268.91i) q^{14} -3156.61 q^{15} +(780.069 + 1351.12i) q^{16} +(-3799.10 - 2193.41i) q^{17} +(1515.90 - 2625.62i) q^{18} +(-11697.8 + 6753.75i) q^{19} -18561.8i q^{20} +(2341.91 + 4806.68i) q^{21} +10926.6 q^{22} +(6367.61 + 11029.0i) q^{23} +(4659.64 + 2690.25i) q^{24} +(12689.9 - 21979.6i) q^{25} +(-2971.91 + 1715.83i) q^{26} +3788.00i q^{27} +(-28264.6 + 13771.1i) q^{28} +6262.53 q^{29} +(19691.8 + 34107.2i) q^{30} +(-17689.7 - 10213.2i) q^{31} +(20777.7 - 35988.0i) q^{32} +(-11822.9 + 6825.94i) q^{33} +54732.5i q^{34} +(-69285.1 - 4873.70i) q^{35} -22274.5 q^{36} +(-7862.08 - 13617.5i) q^{37} +(145949. + 84263.6i) q^{38} +(2143.79 - 3713.16i) q^{39} +(-60529.5 + 34946.7i) q^{40} -69941.8i q^{41} +(37326.8 - 55289.8i) q^{42} +113322. q^{43} +(-40138.5 - 69521.9i) q^{44} +(-42614.2 - 24603.3i) q^{45} +(79445.9 - 137604. i) q^{46} +(-40116.2 + 23161.1i) q^{47} +24320.1i q^{48} +(43981.8 + 109119. i) q^{49} -316653. q^{50} +(-34191.9 - 59222.2i) q^{51} +(21834.4 + 12606.1i) q^{52} +(-64013.2 + 110874. i) q^{53} +(40929.4 - 23630.6i) q^{54} -177340. i q^{55} +(98121.9 + 66243.2i) q^{56} -210561. q^{57} +(-39067.4 - 67666.8i) q^{58} +(242870. + 140221. i) q^{59} +(144675. - 250584. i) q^{60} +(84759.3 - 48935.8i) q^{61} +254850. i q^{62} +(-5848.55 + 83143.6i) q^{63} -418619. q^{64} +(27848.2 + 48234.5i) q^{65} +(147509. + 85164.3i) q^{66} +(-87278.8 + 151171. i) q^{67} +(348243. - 201058. i) q^{68} +198522. i q^{69} +(379559. + 779030. i) q^{70} +345712. q^{71} +(41936.8 + 72636.7i) q^{72} +(-104589. - 60384.4i) q^{73} +(-98091.8 + 169900. i) q^{74} +(342627. - 197816. i) q^{75} -1.23816e6i q^{76} +(-270042. + 131570. i) q^{77} -53494.3 q^{78} +(-381933. - 661527. i) q^{79} +(-273597. - 157961. i) q^{80} +(-29524.5 + 51137.9i) q^{81} +(-755722. + 436316. i) q^{82} +859402. i q^{83} +(-488908. - 34391.1i) q^{84} +888317. q^{85} +(-706933. - 1.22444e6i) q^{86} +(84544.2 + 48811.6i) q^{87} +(-151140. + 261781. i) q^{88} +(-155778. + 89938.3i) q^{89} +613930. i q^{90} +(52787.6 - 78190.9i) q^{91} -1.16737e6 q^{92} +(-159207. - 275755. i) q^{93} +(500512. + 288971. i) q^{94} +(1.36761e6 - 2.36877e6i) q^{95} +(560997. - 323892. i) q^{96} +340171. i q^{97} +(904659. - 1.15594e6i) q^{98} -212812. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} - 42 q^{5} + 748 q^{7} - 454 q^{8} + 972 q^{9}+O(q^{10}) $ 8 * q - 5 * q^2 + 108 * q^3 - 173 * q^4 - 42 * q^5 + 748 * q^7 - 454 * q^8 + 972 * q^9	\( 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} - 42 q^{5} + 748 q^{7} - 454 q^{8} + 972 q^{9} + 261 q^{10} - 1070 q^{11} - 4671 q^{12} + 6070 q^{14} - 756 q^{15} + 3911 q^{16} + 7212 q^{17} + 1215 q^{18} - 24606 q^{19} + 8154 q^{21} - 78 q^{22} - 15224 q^{23} - 6129 q^{24} + 22274 q^{25} - 19044 q^{26} - 3415 q^{28} + 32524 q^{29} + 2349 q^{30} + 40200 q^{31} + 70203 q^{32} - 28890 q^{33} - 242436 q^{35} - 84078 q^{36} - 45670 q^{37} + 503310 q^{38} + 93366 q^{39} - 94941 q^{40} + 55161 q^{42} - 445660 q^{43} - 188829 q^{44} - 10206 q^{45} + 525804 q^{46} + 82884 q^{47} + 24116 q^{49} - 1218884 q^{50} + 64908 q^{51} + 722856 q^{52} - 13034 q^{53} + 32805 q^{54} + 127061 q^{56} - 442908 q^{57} - 159501 q^{58} + 1810362 q^{59} + 429705 q^{60} - 392856 q^{61} + 38394 q^{63} - 1410446 q^{64} - 389004 q^{65} - 1053 q^{66} + 384094 q^{67} - 1616346 q^{68} + 406005 q^{70} + 225688 q^{71} - 55161 q^{72} + 903078 q^{73} + 1185530 q^{74} + 601398 q^{75} - 327674 q^{77} - 342792 q^{78} - 559592 q^{79} + 847713 q^{80} - 236196 q^{81} + 347634 q^{82} - 879444 q^{84} + 1953576 q^{85} - 2302402 q^{86} + 439074 q^{87} + 304887 q^{88} - 1770036 q^{89} - 2960718 q^{91} - 113064 q^{92} + 361800 q^{93} - 1837620 q^{94} + 1160112 q^{95} + 1895481 q^{96} + 5732467 q^{98} - 520020 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 + 108 * q^3 - 173 * q^4 - 42 * q^5 + 748 * q^7 - 454 * q^8 + 972 * q^9 + 261 * q^10 - 1070 * q^11 - 4671 * q^12 + 6070 * q^14 - 756 * q^15 + 3911 * q^16 + 7212 * q^17 + 1215 * q^18 - 24606 * q^19 + 8154 * q^21 - 78 * q^22 - 15224 * q^23 - 6129 * q^24 + 22274 * q^25 - 19044 * q^26 - 3415 * q^28 + 32524 * q^29 + 2349 * q^30 + 40200 * q^31 + 70203 * q^32 - 28890 * q^33 - 242436 * q^35 - 84078 * q^36 - 45670 * q^37 + 503310 * q^38 + 93366 * q^39 - 94941 * q^40 + 55161 * q^42 - 445660 * q^43 - 188829 * q^44 - 10206 * q^45 + 525804 * q^46 + 82884 * q^47 + 24116 * q^49 - 1218884 * q^50 + 64908 * q^51 + 722856 * q^52 - 13034 * q^53 + 32805 * q^54 + 127061 * q^56 - 442908 * q^57 - 159501 * q^58 + 1810362 * q^59 + 429705 * q^60 - 392856 * q^61 + 38394 * q^63 - 1410446 * q^64 - 389004 * q^65 - 1053 * q^66 + 384094 * q^67 - 1616346 * q^68 + 406005 * q^70 + 225688 * q^71 - 55161 * q^72 + 903078 * q^73 + 1185530 * q^74 + 601398 * q^75 - 327674 * q^77 - 342792 * q^78 - 559592 * q^79 + 847713 * q^80 - 236196 * q^81 + 347634 * q^82 - 879444 * q^84 + 1953576 * q^85 - 2302402 * q^86 + 439074 * q^87 + 304887 * q^88 - 1770036 * q^89 - 2960718 * q^91 - 113064 * q^92 + 361800 * q^93 - 1837620 * q^94 + 1160112 * q^95 + 1895481 * q^96 + 5732467 * q^98 - 520020 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−6.23828	−	10.8050i	−0.779785	−	1.35063i	−0.932065	−	0.362290i	$-0.881995\pi$
$2$	−6.23828	−	10.8050i	−0.779785	−	1.35063i	0.152280	−	0.988337i	$-0.451338\pi$
$3$	13.5000	+	7.79423i	0.500000	+	0.288675i
$3$	13.5000	+	7.79423i	0.500000	+	0.288675i
$4$	−45.8323	+	79.3839i	−0.716130	+	1.24037i
$5$	−175.367	+	101.248i	−1.40294	+	0.809986i	−0.994693	−	0.102887i	$-0.967192\pi$
$5$	−175.367	+	101.248i	−1.40294	+	0.809986i	−0.408243	+	0.912873i	$0.633859\pi$
$6$		−	194.490i		−	0.900418i
$7$	284.280	+	191.921i	0.828806	+	0.559536i
$7$	284.280	+	191.921i	0.828806	+	0.559536i
$8$	345.159			0.674138
$9$	121.500	+	210.444i	0.166667	+	0.288675i
$10$	2187.98	+	1263.23i	2.18798	+	1.26323i
$11$	−437.884	+	758.438i	−0.328989	+	0.569826i	−0.982312	−	0.187254i	$-0.940041\pi$
$11$	−437.884	+	758.438i	−0.328989	+	0.569826i	0.653323	+	0.757080i	$0.273375\pi$
$12$	−1237.47	+	714.455i	−0.716130	+	0.413458i
$13$		−	275.049i		−	0.125193i	−0.998039	−	0.0625964i	$-0.980062\pi$
$13$		−	275.049i		−	0.125193i	0.998039	−	0.0625964i	$-0.0199381\pi$
$14$	300.287	−	4268.91i	0.109434	−	1.55573i
$15$	−3156.61			−0.935291
$16$	780.069	+	1351.12i	0.190447	+	0.329863i
$17$	−3799.10	−	2193.41i	−0.773276	−	0.446451i	0.0607662	−	0.998152i	$-0.480646\pi$
$17$	−3799.10	−	2193.41i	−0.773276	−	0.446451i	−0.834042	+	0.551701i	$0.813979\pi$
$18$	1515.90	−	2625.62i	0.259928	−	0.450209i
$19$	−11697.8	+	6753.75i	−1.70547	+	0.984655i	−0.765482	+	0.643458i	$0.777499\pi$
$19$	−11697.8	+	6753.75i	−1.70547	+	0.984655i	−0.939992	+	0.341198i	$0.889167\pi$
$20$		−	18561.8i		−	2.32022i
$21$	2341.91	+	4806.68i	0.252879	+	0.519024i
$22$	10926.6			1.02616
$23$	6367.61	+	11029.0i	0.523351	+	0.906470i	0.999631	+	0.0271766i	$0.00865163\pi$
$23$	6367.61	+	11029.0i	0.523351	+	0.906470i	−0.476280	+	0.879294i	$0.658015\pi$
$24$	4659.64	+	2690.25i	0.337069	+	0.194607i
$25$	12689.9	−	21979.6i	0.812154	−	1.40669i
$26$	−2971.91	+	1715.83i	−0.169089	+	0.0976235i
$27$			3788.00i			0.192450i
$28$	−28264.6	+	13771.1i	−1.28757	+	0.627328i
$29$	6262.53			0.256777			0.128388	−	0.991724i	$-0.459020\pi$
$29$	6262.53			0.256777			0.128388	+	0.991724i	$0.459020\pi$
$30$	19691.8	+	34107.2i	0.729326	+	1.26323i
$31$	−17689.7	−	10213.2i	−0.593793	−	0.342827i	0.172803	−	0.984956i	$-0.444718\pi$
$31$	−17689.7	−	10213.2i	−0.593793	−	0.342827i	−0.766596	+	0.642130i	$0.778051\pi$
$32$	20777.7	−	35988.0i	0.634084	−	1.09827i
$33$	−11822.9	+	6825.94i	−0.328989	+	0.189942i
$34$			54732.5i			1.39254i
$35$	−69285.1	−	4873.70i	−1.61598	−	0.113672i
$36$	−22274.5			−0.477420
$37$	−7862.08	−	13617.5i	−0.155215	−	0.268840i	0.777923	−	0.628360i	$-0.216274\pi$
$37$	−7862.08	−	13617.5i	−0.155215	−	0.268840i	−0.933137	+	0.359521i	$0.882940\pi$
$38$	145949.	+	84263.6i	2.65981	+	1.53564i
$39$	2143.79	−	3713.16i	0.0361400	−	0.0625964i
$40$	−60529.5	+	34946.7i	−0.945773	+	0.546042i
$41$		−	69941.8i		−	1.01481i	−0.861707	−	0.507405i	$-0.830605\pi$
$41$		−	69941.8i		−	1.01481i	0.861707	−	0.507405i	$-0.169395\pi$
$42$	37326.8	−	55289.8i	0.503816	−	0.746272i
$43$	113322.			1.42530			0.712652	−	0.701517i	$-0.247494\pi$
$43$	113322.			1.42530			0.712652	+	0.701517i	$0.247494\pi$
$44$	−40138.5	−	69521.9i	−0.471197	−	0.816138i
$45$	−42614.2	−	24603.3i	−0.467645	−	0.269995i
$46$	79445.9	−	137604.i	0.816202	−	1.41370i
$47$	−40116.2	+	23161.1i	−0.386390	+	0.223083i	−0.680595	−	0.732660i	$-0.738279\pi$
$47$	−40116.2	+	23161.1i	−0.386390	+	0.223083i	0.294205	+	0.955742i	$0.404945\pi$
$48$			24320.1i			0.219909i
$49$	43981.8	+	109119.i	0.373839	+	0.927494i
$50$	−316653.			−2.53322
$51$	−34191.9	−	59222.2i	−0.257759	−	0.446451i
$52$	21834.4	+	12606.1i	0.155286	+	0.0896543i
$53$	−64013.2	+	110874.i	−0.429973	+	0.744736i	−0.996870	−	0.0790529i	$-0.974810\pi$
$53$	−64013.2	+	110874.i	−0.429973	+	0.744736i	0.566897	+	0.823789i	$0.308144\pi$
$54$	40929.4	−	23630.6i	0.259928	−	0.150070i
$55$		−	177340.i		−	1.06591i
$56$	98121.9	+	66243.2i	0.558730	+	0.377205i
$57$	−210561.			−1.13698
$58$	−39067.4	−	67666.8i	−0.200231	−	0.346810i
$59$	242870.	+	140221.i	1.18254	+	0.682742i	0.956602	−	0.291398i	$-0.0941205\pi$
$59$	242870.	+	140221.i	1.18254	+	0.682742i	0.225942	+	0.974141i	$0.427454\pi$
$60$	144675.	−	250584.i	0.669789	−	1.16011i
$61$	84759.3	−	48935.8i	0.373420	−	0.215594i	−0.301531	−	0.953456i	$-0.597498\pi$
$61$	84759.3	−	48935.8i	0.373420	−	0.215594i	0.674952	+	0.737862i	$0.264164\pi$
$62$			254850.i			1.06932i
$63$	−5848.55	+	83143.6i	−0.0233898	+	0.332512i
$64$	−418619.			−1.59690
$65$	27848.2	+	48234.5i	0.101404	+	0.175638i
$66$	147509.	+	85164.3i	0.513081	+	0.296228i
$67$	−87278.8	+	151171.i	−0.290191	+	0.502626i	−0.973855	−	0.227171i	$-0.927052\pi$
$67$	−87278.8	+	151171.i	−0.290191	+	0.502626i	0.683663	+	0.729797i	$0.260386\pi$
$68$	348243.	−	201058.i	1.10753	−	0.639433i
$69$			198522.i			0.604314i
$70$	379559.	+	779030.i	1.10659	+	2.27122i
$71$	345712.			0.965915			0.482957	−	0.875644i	$-0.339563\pi$
$71$	345712.			0.965915			0.482957	+	0.875644i	$0.339563\pi$
$72$	41936.8	+	72636.7i	0.112356	+	0.194607i
$73$	−104589.	−	60384.4i	−0.268854	−	0.155223i	0.359513	−	0.933140i	$-0.382943\pi$
$73$	−104589.	−	60384.4i	−0.268854	−	0.155223i	−0.628367	+	0.777917i	$0.716276\pi$
$74$	−98091.8	+	169900.i	−0.242068	+	0.419274i
$75$	342627.	−	197816.i	0.812154	−	0.468897i
$76$		−	1.23816e6i		−	2.82056i
$77$	−270042.	+	131570.i	−0.591506	+	0.288194i
$78$	−53494.3			−0.112726
$79$	−381933.	−	661527.i	−0.774650	−	1.34173i	−0.934991	−	0.354671i	$-0.884593\pi$
$79$	−381933.	−	661527.i	−0.774650	−	1.34173i	0.160341	−	0.987062i	$-0.448741\pi$
$80$	−273597.	−	157961.i	−0.534369	−	0.308518i
$81$	−29524.5	+	51137.9i	−0.0555556	+	0.0962250i
$82$	−755722.	+	436316.i	−1.37063	+	0.791334i
$83$			859402.i			1.50301i	0.659727	+	0.751505i	$0.270672\pi$
$83$			859402.i			1.50301i	−0.659727	+	0.751505i	$0.729328\pi$
$84$	−488908.	−	34391.1i	−0.824877	−	0.0580241i
$85$	888317.			1.44648
$86$	−706933.	−	1.22444e6i	−1.11143	−	1.92506i
$87$	84544.2	+	48811.6i	0.128388	+	0.0741251i
$88$	−151140.	+	261781.i	−0.221784	+	0.384141i
$89$	−155778.	+	89938.3i	−0.220971	+	0.127578i	−0.606400	−	0.795160i	$-0.707387\pi$
$89$	−155778.	+	89938.3i	−0.220971	+	0.127578i	0.385429	+	0.922738i	$0.374054\pi$
$90$			613930.i			0.842153i
$91$	52787.6	−	78190.9i	0.0700499	−	0.103761i
$92$	−1.16737e6			−1.49915
$93$	−159207.	−	275755.i	−0.197931	−	0.342827i
$94$	500512.	+	288971.i	0.602603	+	0.347913i
$95$	1.36761e6	−	2.36877e6i	1.59511	−	2.76282i
$96$	560997.	−	323892.i	0.634084	−	0.366088i
$97$			340171.i			0.372720i	0.982482	+	0.186360i	$0.0596690\pi$
$97$			340171.i			0.372720i	−0.982482	+	0.186360i	$0.940331\pi$
$98$	904659.	−	1.15594e6i	0.961184	−	1.22816i
$99$	−212812.			−0.219326
$100$	1.16321e6	+	2.01475e6i	1.16321	+	2.01475i
$101$	903587.	+	521686.i	0.877013	+	0.506344i	0.869672	−	0.493630i	$-0.164330\pi$
$101$	903587.	+	521686.i	0.877013	+	0.506344i	0.00734043	+	0.999973i	$0.497663\pi$
$102$	−426598.	+	738889.i	−0.401993	+	0.696272i
$103$	−675522.	+	390013.i	−0.618198	+	0.356917i	−0.776167	−	0.630527i	$-0.782839\pi$
$103$	−675522.	+	390013.i	−0.618198	+	0.356917i	0.157969	+	0.987444i	$0.449505\pi$
$104$		−	94935.5i		−	0.0843973i
$105$	−897362.	−	605819.i	−0.775175	−	0.523329i
$106$	1.59733e6			1.34115
$107$	498844.	+	864024.i	0.407205	+	0.705301i	0.994575	−	0.104018i	$-0.0331700\pi$
$107$	498844.	+	864024.i	0.407205	+	0.705301i	−0.587370	+	0.809319i	$0.699837\pi$
$108$	−300706.	−	173612.i	−0.238710	−	0.137819i
$109$	−727835.	+	1.26065e6i	−0.562023	+	0.973452i	0.435297	+	0.900287i	$0.356643\pi$
$109$	−727835.	+	1.26065e6i	−0.562023	+	0.973452i	−0.997320	+	0.0731648i	$0.976690\pi$
$110$	−1.91616e6	+	1.10630e6i	−1.43964	+	0.831177i
$111$		−	245116.i		−	0.179226i
$112$	−37549.5	+	533808.i	−0.0267270	+	0.379954i
$113$	177612.			0.123094			0.0615469	−	0.998104i	$-0.480397\pi$
$113$	177612.			0.123094			0.0615469	+	0.998104i	$0.480397\pi$
$114$	1.31354e6	+	2.27512e6i	0.886602	+	1.53564i
$115$	−2.23334e6	−	1.28942e6i	−1.46846	−	0.847814i
$116$	−287026.	+	497144.i	−0.183886	+	0.318499i
$117$	57882.4	−	33418.4i	0.0361400	−	0.0208655i
$118$		−	3.49895e6i		−	2.12957i
$119$	−659049.	−	1.35267e6i	−0.391090	−	0.802697i
$120$	−1.08953e6			−0.630516
$121$	502295.	+	870001.i	0.283533	+	0.491093i
$122$	−1.05750e6	−	610551.i	−0.582375	−	0.336234i
$123$	545142.	−	944214.i	0.292951	−	0.507405i
$124$	1.62152e6	−	936184.i	0.850466	−	0.491017i
$125$			1.97531e6i			1.01136i
$126$	934853.	−	455479.i	0.467338	−	0.227697i
$127$	924373.			0.451269			0.225635	−	0.974212i	$-0.427554\pi$
$127$	924373.			0.451269			0.225635	+	0.974212i	$0.427554\pi$
$128$	1.28169e6	+	2.21995e6i	0.611158	+	1.05856i
$129$	1.52984e6	+	883255.i	0.712652	+	0.411450i
$130$	347450.	−	601800.i	0.158147	−	0.273919i
$131$	837624.	−	483602.i	0.372593	−	0.215117i	−0.301997	−	0.953309i	$-0.597653\pi$
$131$	837624.	−	483602.i	0.372593	−	0.215117i	0.674591	+	0.738192i	$0.264320\pi$
$132$		−	1.25139e6i		−	0.544092i
$133$	−4.62165e6	−	325100.i	−1.96446	−	0.138185i
$134$	2.17788e6			0.905148
$135$	−383528.	−	664290.i	−0.155882	−	0.269995i
$136$	−1.31129e6	−	757076.i	−0.521295	−	0.300970i
$137$	−2.35006e6	+	4.07043e6i	−0.913940	+	1.58299i	−0.105493	+	0.994420i	$0.533642\pi$
$137$	−2.35006e6	+	4.07043e6i	−0.913940	+	1.58299i	−0.808446	+	0.588570i	$0.799691\pi$
$138$	2.14504e6	−	1.23844e6i	0.816202	−	0.471235i
$139$			1.64306e6i			0.611798i	0.952064	+	0.305899i	$0.0989570\pi$
$139$			1.64306e6i			0.611798i	−0.952064	+	0.305899i	$0.901043\pi$
$140$	3.56239e6	−	5.27674e6i	1.29825	−	1.92301i
$141$	−722092.			−0.257594
$142$	−2.15665e6	−	3.73542e6i	−0.753206	−	1.30459i
$143$	208607.	+	120439.i	0.0713381	+	0.0411870i
$144$	−189557.	+	328322.i	−0.0634822	+	0.109954i
$145$	−1.09824e6	+	634070.i	−0.360242	+	0.207986i
$146$			1.50678e6i			0.484162i
$147$	−256742.	+	1.81591e6i	−0.0808249	+	0.571665i
$148$	1.44135e6			0.444615
$149$	−2.31369e6	−	4.00743e6i	−0.699433	−	1.21145i	−0.968663	−	0.248378i	$-0.920103\pi$
$149$	−2.31369e6	−	4.00743e6i	−0.699433	−	1.21145i	0.269230	−	0.963076i	$-0.413231\pi$
$150$	−4.27481e6	−	2.46806e6i	−1.26661	−	0.731278i
$151$	2.24610e6	−	3.89036e6i	0.652377	−	1.12995i	−0.330168	−	0.943922i	$-0.607105\pi$
$151$	2.24610e6	−	3.89036e6i	0.652377	−	1.12995i	0.982545	−	0.186028i	$-0.0595614\pi$
$152$	−4.03761e6	+	2.33112e6i	−1.14972	+	0.663794i
$153$		−	1.06600e6i		−	0.297634i
$154$	3.10621e6	+	2.09704e6i	0.850490	+	0.574175i
$155$	4.13625e6			1.11074
$156$	196510.	+	340365.i	0.0517619	+	0.0896543i
$157$	−4.17859e6	−	2.41251e6i	−1.07977	−	0.623405i	−0.148935	−	0.988847i	$-0.547584\pi$
$157$	−4.17859e6	−	2.41251e6i	−1.07977	−	0.623405i	−0.930834	+	0.365442i	$0.880918\pi$
$158$	−4.76521e6	+	8.25358e6i	−1.20812	+	2.09253i
$159$	−1.72836e6	+	997866.i	−0.429973	+	0.248245i
$160$			8.41480e6i			2.05440i
$161$	−306513.	+	4.35741e6i	−0.0734464	+	1.04412i
$162$	736728.			0.173286
$163$	1.69763e6	+	2.94038e6i	0.391994	+	0.678954i	0.992713	−	0.120507i	$-0.0384519\pi$
$163$	1.69763e6	+	2.94038e6i	0.391994	+	0.678954i	−0.600718	+	0.799461i	$0.705119\pi$
$164$	5.55225e6	+	3.20559e6i	1.25874	+	0.726736i
$165$	1.38223e6	−	2.39409e6i	0.307700	−	0.532953i
$166$	9.28585e6	−	5.36119e6i	2.03001	−	1.17203i
$167$		−	2.04579e6i		−	0.439249i	−0.975584	−	0.219625i	$-0.929517\pi$
$167$		−	2.04579e6i		−	0.439249i	0.975584	−	0.219625i	$-0.0704832\pi$
$168$	808331.	+	1.65907e6i	0.170475	+	0.349894i
$169$	4.75116e6			0.984327
$170$	−5.54157e6	−	9.59828e6i	−1.12794	−	1.95365i
$171$	−2.84258e6	−	1.64116e6i	−0.568491	−	0.328218i
$172$	−5.19379e6	+	8.99591e6i	−1.02070	+	1.76791i
$173$	−272758.	+	157477.i	−0.0526792	+	0.0304144i	−0.526108	−	0.850418i	$-0.676349\pi$
$173$	−272758.	+	157477.i	−0.0526792	+	0.0304144i	0.473429	+	0.880832i	$0.343016\pi$
$174$		−	1.21800e6i		−	0.231207i
$175$	7.82583e6	−	3.81290e6i	1.46021	−	0.711445i
$176$	−1.36632e6			−0.250619
$177$	2.18583e6	+	3.78596e6i	0.394181	+	0.682742i
$178$	1.94357e6	+	1.12212e6i	0.344620	+	0.198966i
$179$	2.01204e6	−	3.48495e6i	0.350814	−	0.607627i	−0.635579	−	0.772036i	$-0.719238\pi$
$179$	2.01204e6	−	3.48495e6i	0.350814	−	0.607627i	0.986392	+	0.164409i	$0.0525717\pi$
$180$	3.90621e6	−	2.25525e6i	0.669789	−	0.386703i
$181$			1.53820e6i			0.259405i	0.991553	+	0.129703i	$0.0414022\pi$
$181$			1.53820e6i			0.259405i	−0.991553	+	0.129703i	$0.958598\pi$
$182$	−1.17416e6	−	82593.5i	−0.194766	−	0.0137004i
$183$	1.52567e6			0.248947
$184$	2.19784e6	+	3.80677e6i	0.352811	+	0.611086i
$185$	2.75750e6	+	1.59204e6i	0.435512	+	0.251443i
$186$	−1.98636e6	+	3.44047e6i	−0.308687	+	0.534662i
$187$	3.32714e6	−	1.92092e6i	0.508798	−	0.293755i
$188$		−	4.24611e6i		−	0.639024i
$189$	−726995.	+	1.07685e6i	−0.107683	+	0.159504i
$190$	−3.41262e7			−4.97538
$191$	−2.13865e6	−	3.70425e6i	−0.306931	−	0.531619i	0.670759	−	0.741676i	$-0.265969\pi$
$191$	−2.13865e6	−	3.70425e6i	−0.306931	−	0.531619i	−0.977689	+	0.210056i	$0.932635\pi$
$192$	−5.65135e6	−	3.26281e6i	−0.798452	−	0.460986i
$193$	3.22312e6	−	5.58261e6i	0.448337	−	0.776543i	−0.549941	−	0.835204i	$-0.685350\pi$
$193$	3.22312e6	−	5.58261e6i	0.448337	−	0.776543i	0.998278	+	0.0586609i	$0.0186831\pi$
$194$	3.67556e6	−	2.12208e6i	0.503406	−	0.290641i
$195$			868220.i			0.117092i
$196$	−1.06780e7	−	1.50972e6i	−1.41815	−	0.200506i
$197$	−2.73215e6			−0.357359			−0.178680	−	0.983907i	$-0.557183\pi$
$197$	−2.73215e6			−0.357359			−0.178680	+	0.983907i	$0.557183\pi$
$198$	1.32758e6	+	2.29943e6i	0.171027	+	0.296228i
$199$	517231.	+	298623.i	0.0656334	+	0.0378935i	0.532458	−	0.846457i	$-0.321269\pi$
$199$	517231.	+	298623.i	0.0656334	+	0.0378935i	−0.466824	+	0.884350i	$0.654602\pi$
$200$	4.38003e6	−	7.58644e6i	0.547504	−	0.948305i
$201$	−2.35653e6	+	1.36054e6i	−0.290191	+	0.167542i
$202$		−	1.30177e7i		−	1.57936i
$203$	1.78032e6	+	1.20191e6i	0.212818	+	0.143676i
$204$	6.26838e6			0.738354
$205$	7.08148e6	+	1.22655e7i	0.821982	+	1.42372i
$206$	8.42819e6	+	4.86602e6i	0.964123	+	0.556637i
$207$	−1.54733e6	+	2.68005e6i	−0.174450	+	0.302157i
$208$	371623.	−	214557.i	0.0412965	−	0.0238425i
$209$		−	1.18294e7i		−	1.29576i
$210$	−947888.	+	1.34753e7i	−0.102353	+	1.45506i
$211$	−3.67602e6			−0.391319			−0.195659	−	0.980672i	$-0.562685\pi$
$211$	−3.67602e6			−0.391319			−0.195659	+	0.980672i	$0.562685\pi$
$212$	−5.86774e6	−	1.01632e7i	−0.615833	−	1.06665i
$213$	4.66711e6	+	2.69455e6i	0.482957	+	0.278836i
$214$	6.22386e6	−	1.07800e7i	0.635066	−	1.09997i
$215$	−1.98729e7	+	1.14736e7i	−1.99961	+	1.15448i
$216$			1.30746e6i			0.129738i
$217$	−3.06872e6	−	6.29842e6i	−0.300316	−	0.616386i
$218$	1.81618e7			1.75303
$219$	−941299.	−	1.63038e6i	−0.0896180	−	0.155223i
$220$	1.40779e7	+	8.12790e6i	1.32212	+	0.763326i
$221$	−603295.	+	1.04494e6i	−0.0558924	+	0.0968086i
$222$	−2.64848e6	+	1.52910e6i	−0.242068	+	0.139758i
$223$			1.43225e7i			1.29153i	0.763535	+	0.645766i	$0.223462\pi$
$223$			1.43225e7i			1.29153i	−0.763535	+	0.645766i	$0.776538\pi$
$224$	1.28135e7	−	6.24301e6i	1.14005	−	0.555456i
$225$	6.16729e6			0.541436
$226$	−1.10799e6	−	1.91910e6i	−0.0959867	−	0.166254i
$227$	−2.62502e6	−	1.51555e6i	−0.224416	−	0.129567i	0.383577	−	0.923509i	$-0.374692\pi$
$227$	−2.62502e6	−	1.51555e6i	−0.224416	−	0.129567i	−0.607994	+	0.793942i	$0.708025\pi$
$228$	9.65050e6	−	1.67152e7i	0.814227	−	1.41028i
$229$	−5.42194e6	+	3.13036e6i	−0.451490	+	0.260668i	−0.708459	−	0.705752i	$-0.750609\pi$
$229$	−5.42194e6	+	3.13036e6i	−0.451490	+	0.260668i	0.256969	+	0.966420i	$0.417276\pi$
$230$			3.21750e7i			2.64445i
$231$	−4.67105e6	−	328575.i	−0.378947	−	0.0266562i
$232$	2.16157e6			0.173103
$233$	5.92360e6	+	1.02600e7i	0.468293	+	0.811107i	0.999343	−	0.0362330i	$-0.0115359\pi$
$233$	5.92360e6	+	1.02600e7i	0.468293	+	0.811107i	−0.531050	+	0.847340i	$0.678203\pi$
$234$	−722173.	−	416947.i	−0.0563629	−	0.0325412i
$235$	4.69004e6	−	8.12339e6i	0.361387	−	0.625941i
$236$	−2.22626e7	+	1.28533e7i	−1.69371	+	0.977864i
$237$		−	1.19075e7i		−	0.894489i
$238$	−1.05043e7	+	1.55594e7i	−0.779178	+	1.15415i
$239$	4.29229e6			0.314410			0.157205	−	0.987566i	$-0.449752\pi$
$239$	4.29229e6			0.314410			0.157205	+	0.987566i	$0.449752\pi$
$240$	−2.46237e6	−	4.26495e6i	−0.178123	−	0.308518i
$241$	1.37366e7	+	7.93085e6i	0.981362	+	0.566589i	0.902681	−	0.430310i	$-0.141596\pi$
$241$	1.37366e7	+	7.93085e6i	0.981362	+	0.566589i	0.0786807	+	0.996900i	$0.474929\pi$
$242$	6.26692e6	−	1.08546e7i	0.442189	−	0.765894i
$243$	−797162.	+	460241.i	−0.0555556	+	0.0320750i
$244$			8.97136e6i			0.617574i
$245$	−1.87610e7	−	1.46827e7i	−1.27573	−	0.998410i
$246$	−1.36030e7			−0.913754
$247$	1.85761e6	+	3.21747e6i	0.123272	+	0.213513i
$248$	−6.10575e6	−	3.52516e6i	−0.400299	−	0.231113i
$249$	−6.69838e6	+	1.16019e7i	−0.433882	+	0.751505i
$250$	2.13433e7	−	1.23226e7i	1.36597	−	0.788644i
$251$		−	7.11752e6i		−	0.450099i	−0.974347	−	0.225049i	$-0.927746\pi$
$251$		−	7.11752e6i		−	0.450099i	0.974347	−	0.225049i	$-0.0722543\pi$
$252$	−6.33220e6	−	4.27494e6i	−0.395688	−	0.267134i
$253$	−1.11531e7			−0.688707
$254$	−5.76650e6	−	9.98786e6i	−0.351893	−	0.609497i
$255$	1.19923e7	+	6.92374e6i	0.723238	+	0.417562i
$256$	2.59529e6	−	4.49518e6i	0.154692	−	0.267934i
$257$	−6.24715e6	+	3.60680e6i	−0.368030	+	0.212482i	−0.672597	−	0.740009i	$-0.734821\pi$
$257$	−6.24715e6	+	3.60680e6i	−0.368030	+	0.212482i	0.304568	+	0.952491i	$0.401488\pi$
$258$		−	2.20400e7i		−	1.28337i
$259$	378451.	−	5.38010e6i	0.0217826	−	0.309664i
$260$	−5.10538e6			−0.290475
$261$	760898.	+	1.31791e6i	0.0427962	+	0.0741251i
$262$	−1.04507e7	−	6.03370e6i	−0.581086	−	0.335490i
$263$	8.28046e6	−	1.43422e7i	0.455184	−	0.788402i	−0.543514	−	0.839400i	$-0.682907\pi$
$263$	8.28046e6	−	1.43422e7i	0.455184	−	0.788402i	0.998699	+	0.0509974i	$0.0162400\pi$
$264$	−4.08077e6	+	2.35603e6i	−0.221784	+	0.128047i
$265$		−	2.59249e7i		−	1.39309i
$266$	2.53185e7	+	5.19651e7i	1.34522	+	2.76100i
$267$	−2.80400e6			−0.147314
$268$	−8.00038e6	−	1.38571e7i	−0.415629	−	0.719891i
$269$	4.73497e6	+	2.73374e6i	0.243254	+	0.140443i	0.616671	−	0.787221i	$-0.288481\pi$
$269$	4.73497e6	+	2.73374e6i	0.243254	+	0.140443i	−0.373417	+	0.927663i	$0.621814\pi$
$270$	−4.78511e6	+	8.28805e6i	−0.243109	+	0.421077i
$271$	−1.61594e7	+	9.32961e6i	−0.811925	+	0.468765i	−0.847624	−	0.530597i	$-0.821968\pi$
$271$	−1.61594e7	+	9.32961e6i	−0.811925	+	0.468765i	0.0356988	+	0.999363i	$0.488634\pi$
$272$		−	6.84405e6i		−	0.340100i
$273$	1.32207e6	−	644139.i	0.0649780	−	0.0316586i
$274$	5.86414e7			2.85071
$275$	1.11134e7	+	1.92490e7i	0.534379	+	0.925572i
$276$	−1.57595e7	−	9.09874e6i	−0.749574	−	0.432767i
$277$	3.81751e6	−	6.61212e6i	0.179614	−	0.311101i	−0.762134	−	0.647419i	$-0.775848\pi$
$277$	3.81751e6	−	6.61212e6i	0.179614	−	0.311101i	0.941748	+	0.336318i	$0.109182\pi$
$278$	1.77532e7	−	1.02498e7i	0.826311	−	0.477071i
$279$		−	4.96359e6i		−	0.228551i
$280$	−2.39144e7	−	1.68220e6i	−1.08939	−	0.0766309i
$281$	−2.86272e7			−1.29021			−0.645103	−	0.764095i	$-0.723186\pi$
$281$	−2.86272e7			−1.29021			−0.645103	+	0.764095i	$0.723186\pi$
$282$	4.50461e6	+	7.80221e6i	0.200868	+	0.347913i
$283$	−1.84385e7	−	1.06455e7i	−0.813518	−	0.469685i	0.0346580	−	0.999399i	$-0.488966\pi$
$283$	−1.84385e7	−	1.06455e7i	−0.813518	−	0.469685i	−0.848176	+	0.529714i	$0.822299\pi$
$284$	−1.58448e7	+	2.74439e7i	−0.691720	+	1.19809i
$285$	3.69255e7	−	2.13189e7i	1.59511	−	0.920939i
$286$		−	3.00534e6i		−	0.128468i
$287$	1.34233e7	−	1.98831e7i	0.567823	−	0.841081i
$288$	1.00979e7			0.422723
$289$	−2.44666e6	−	4.23774e6i	−0.101363	−	0.175566i
$290$	1.37023e7	+	7.91102e6i	0.561822	+	0.324368i
$291$	−2.65137e6	+	4.59231e6i	−0.107595	+	0.186360i
$292$	9.58709e6	−	5.53511e6i	0.385069	−	0.222319i
$293$		−	1.72102e7i		−	0.684199i	−0.939664	−	0.342100i	$-0.888862\pi$
$293$		−	1.72102e7i		−	0.684199i	0.939664	−	0.342100i	$-0.111138\pi$
$294$	2.12225e7	−	8.55403e6i	0.835132	−	0.336611i
$295$	−5.67885e7			−2.21205
$296$	−2.71367e6	−	4.70021e6i	−0.104636	−	0.181235i
$297$	−2.87296e6	−	1.65870e6i	−0.109663	−	0.0633139i
$298$	−2.88669e7	+	4.99989e7i	−1.09082	+	1.88935i
$299$	3.03352e6	−	1.75140e6i	0.113484	−	0.0655198i
$300$			3.62654e7i			1.34316i
$301$	3.22151e7	+	2.17488e7i	1.18130	+	0.797509i
$302$	−5.60472e7			−2.03485
$303$	8.13228e6	+	1.40855e7i	0.292338	+	0.506344i
$304$	−1.82502e7	−	1.05368e7i	−0.649603	−	0.375048i
$305$	−9.90933e6	+	1.71635e7i	−0.349257	+	0.604930i
$306$	−1.15181e7	+	6.65000e6i	−0.401993	+	0.232091i
$307$			4.11253e7i			1.42133i	0.703533	+	0.710663i	$0.251605\pi$
$307$			4.11253e7i			1.42133i	−0.703533	+	0.710663i	$0.748395\pi$
$308$	1.93211e6	−	2.74671e7i	0.0661272	−	0.940072i
$309$	−1.21594e7			−0.412132
$310$	−2.58031e7	−	4.46923e7i	−0.866138	−	1.50019i
$311$	9.88085e6	+	5.70471e6i	0.328483	+	0.189650i	0.655167	−	0.755484i	$-0.272598\pi$
$311$	9.88085e6	+	5.70471e6i	0.328483	+	0.189650i	−0.326684	+	0.945133i	$0.605931\pi$
$312$	739949.	−	1.28163e6i	0.0243634	−	0.0421986i
$313$	−930200.	+	537051.i	−0.0303350	+	0.0175139i	−0.515091	−	0.857136i	$-0.672242\pi$
$313$	−930200.	+	537051.i	−0.0303350	+	0.0175139i	0.484756	+	0.874650i	$0.338908\pi$
$314$			6.01997e7i			1.94449i
$315$	−7.39249e6	−	1.51728e7i	−0.236515	−	0.485438i
$316$	7.00194e7			2.21900
$317$	9.89978e6	+	1.71469e7i	0.310776	+	0.538280i	0.978531	−	0.206101i	$-0.0660777\pi$
$317$	9.89978e6	+	1.71469e7i	0.310776	+	0.538280i	−0.667754	+	0.744382i	$0.732744\pi$
$318$	2.15639e7	+	1.24499e7i	0.670574	+	0.387156i
$319$	−2.74226e6	+	4.74974e6i	−0.0844768	+	0.146318i
$320$	7.34119e7	−	4.23844e7i	2.24035	−	1.29347i
$321$			1.55524e7i			0.470200i
$322$	4.89940e7	−	2.38709e7i	1.46749	−	0.714992i
$323$	5.92551e7			1.75840
$324$	−2.70635e6	−	4.68754e6i	−0.0795699	−	0.137819i
$325$	−6.04545e6	−	3.49034e6i	−0.176108	−	0.101676i
$326$	2.11806e7	−	3.66858e7i	0.611343	−	1.05888i
$327$	−1.96516e7	+	1.13458e7i	−0.562023	+	0.324484i
$328$		−	2.41410e7i		−	0.684123i
$329$	−1.58494e7	−	1.11489e6i	−0.445065	−	0.0313071i
$330$	−3.44909e7			−0.959761
$331$	9.56610e6	+	1.65690e7i	0.263785	+	0.456890i	0.967245	−	0.253846i	$-0.0816956\pi$
$331$	9.56610e6	+	1.65690e7i	0.263785	+	0.456890i	−0.703459	+	0.710736i	$0.748362\pi$
$332$	−6.82226e7	−	3.93884e7i	−1.86429	−	1.07635i
$333$	1.91049e6	−	3.30906e6i	0.0517382	−	0.0896132i
$334$	−2.21048e7	+	1.27622e7i	−0.593262	+	0.342520i
$335$		−	3.53473e7i		−	0.940204i
$336$	−4.66754e6	+	6.91374e6i	−0.123047	+	0.182262i
$337$	6.12984e7			1.60162			0.800810	−	0.598919i	$-0.204403\pi$
$337$	6.12984e7			1.60162			0.800810	+	0.598919i	$0.204403\pi$
$338$	−2.96391e7	−	5.13363e7i	−0.767563	−	1.32946i
$339$	2.39776e6	+	1.38435e6i	0.0615469	+	0.0355341i
$340$	−4.07136e7	+	7.05180e7i	−1.03586	+	1.79417i
$341$	1.54921e7	−	8.94435e6i	0.390703	−	0.225572i
$342$			4.09521e7i			1.02376i
$343$	−8.43899e6	+	3.94613e7i	−0.209126	+	0.977889i
$344$	3.91140e7			0.960853
$345$	−2.01000e7	−	3.48143e7i	−0.489485	−	0.847814i
$346$	3.40308e6	+	1.96477e6i	0.0821569	+	0.0474333i
$347$	−3.87907e7	+	6.71875e7i	−0.928409	+	1.60805i	−0.142424	+	0.989806i	$0.545490\pi$
$347$	−3.87907e7	+	6.71875e7i	−0.928409	+	1.60805i	−0.785985	+	0.618246i	$0.787844\pi$
$348$	−7.74971e6	+	4.47430e6i	−0.183886	+	0.106166i
$349$		−	3.32443e7i		−	0.782061i	−0.920378	−	0.391031i	$-0.872119\pi$
$349$		−	3.32443e7i		−	0.782061i	0.920378	−	0.391031i	$-0.127881\pi$
$350$	−9.00182e7	−	6.07723e7i	−2.09955	−	1.41743i
$351$	1.04188e6			0.0240934
$352$	1.81964e7	+	3.15171e7i	0.417213	+	0.722634i
$353$	−1.68383e7	−	9.72160e6i	−0.382802	−	0.221011i	0.296235	−	0.955115i	$-0.404269\pi$
$353$	−1.68383e7	−	9.72160e6i	−0.382802	−	0.221011i	−0.679037	+	0.734104i	$0.737602\pi$
$354$	2.72716e7	−	4.72358e7i	0.614754	−	1.06478i
$355$	−6.06264e7	+	3.50027e7i	−1.35512	+	0.782377i
$356$		−	1.64883e7i		−	0.365448i
$357$	1.64587e6	−	2.33979e7i	0.0361735	−	0.514246i
$358$	−5.02066e7			−1.09424
$359$	−1.27237e7	−	2.20381e7i	−0.274999	−	0.476311i	0.695136	−	0.718878i	$-0.255344\pi$
$359$	−1.27237e7	−	2.20381e7i	−0.274999	−	0.476311i	−0.970135	+	0.242567i	$0.922011\pi$
$360$	−1.47087e7	−	8.49205e6i	−0.315258	−	0.182014i
$361$	6.77034e7	−	1.17266e8i	1.43909	−	2.49258i
$362$	1.66203e7	−	9.59575e6i	0.350360	−	0.202280i
$363$			1.56600e7i			0.327395i
$364$	3.78772e6	+	7.77415e6i	0.0785370	+	0.161194i
$365$	2.44552e7			0.502914
$366$	−9.51754e6	−	1.64849e7i	−0.194125	−	0.336234i
$367$	−7.02719e6	−	4.05715e6i	−0.142162	−	0.0820773i	0.427232	−	0.904142i	$-0.359489\pi$
$367$	−7.02719e6	−	4.05715e6i	−0.142162	−	0.0820773i	−0.569394	+	0.822065i	$0.692822\pi$
$368$	−9.93435e6	+	1.72068e7i	−0.199341	+	0.345268i
$369$	1.47188e7	−	8.49793e6i	0.292951	−	0.169135i
$370$		−	3.97265e7i		−	0.784287i
$371$	−3.94767e7	+	1.92339e7i	−0.773071	+	0.376656i
$372$	2.91873e7			0.566977
$373$	3.60324e7	+	6.24099e7i	0.694330	+	1.20262i	0.970406	+	0.241480i	$0.0776327\pi$
$373$	3.60324e7	+	6.24099e7i	0.694330	+	1.20262i	−0.276076	+	0.961136i	$0.589034\pi$
$374$	−4.15112e7	−	2.39665e7i	−0.793507	−	0.458131i
$375$	−1.53960e7	+	2.66667e7i	−0.291955	+	0.505680i
$376$	−1.38465e7	+	7.99426e6i	−0.260481	+	0.150389i
$377$		−	1.72250e6i		−	0.0321466i
$378$	1.61706e7	+	1.13749e6i	0.299400	+	0.0210606i
$379$	4.53715e7			0.833423			0.416711	−	0.909039i	$-0.363183\pi$
$379$	4.53715e7			0.833423			0.416711	+	0.909039i	$0.363183\pi$
$380$	1.25361e8	+	2.17132e8i	2.28462	+	3.95707i
$381$	1.24790e7	+	7.20477e6i	0.225635	+	0.130270i
$382$	−2.66830e7	+	4.62164e7i	−0.478680	+	0.829098i
$383$	6.55862e7	−	3.78662e7i	1.16739	−	0.673994i	0.214327	−	0.976762i	$-0.431244\pi$
$383$	6.55862e7	−	3.78662e7i	1.16739	−	0.673994i	0.953064	+	0.302768i	$0.0979108\pi$
$384$			3.99592e7i			0.705704i
$385$	3.40352e7	−	5.04143e7i	0.596412	−	0.883429i
$386$	−8.04269e7			−1.39843
$387$	1.37686e7	+	2.38479e7i	0.237551	+	0.411450i
$388$	−2.70041e7	−	1.55908e7i	−0.462311	−	0.266916i
$389$	−4.41471e6	+	7.64649e6i	−0.0749986	+	0.129901i	−0.901086	−	0.433641i	$-0.857229\pi$
$389$	−4.41471e6	+	7.64649e6i	−0.0749986	+	0.129901i	0.826087	+	0.563542i	$0.190562\pi$
$390$	9.38114e6	−	5.41620e6i	0.158147	−	0.0913064i
$391$		−	5.58672e7i		−	0.934602i
$392$	1.51807e7	+	3.76633e7i	0.252019	+	0.625259i
$393$	1.50772e7			0.248396
$394$	1.70439e7	+	2.95209e7i	0.278664	+	0.482659i
$395$	1.33957e8	+	7.73400e7i	2.17357	+	1.25491i
$396$	9.75365e6	−	1.68938e7i	0.157066	−	0.272046i
$397$	−3.45140e7	+	1.99267e7i	−0.551599	+	0.318466i	−0.749767	−	0.661702i	$-0.769834\pi$
$397$	−3.45140e7	+	1.99267e7i	−0.551599	+	0.318466i	0.198167	+	0.980168i	$0.436501\pi$
$398$		−	7.45158e6i		−	0.118195i
$399$	−5.98584e7	−	4.04111e7i	−0.942338	−	0.636182i
$400$	3.95960e7			0.618687
$401$	1.65566e6	+	2.86769e6i	0.0256767	+	0.0444733i	0.878578	−	0.477599i	$-0.158493\pi$
$401$	1.65566e6	+	2.86769e6i	0.0256767	+	0.0444733i	−0.852902	+	0.522072i	$0.825159\pi$
$402$	2.94014e7	+	1.69749e7i	0.452574	+	0.261294i
$403$	−2.80911e6	+	4.86553e6i	−0.0429194	+	0.0743386i
$404$	−8.28269e7	+	4.78202e7i	−1.25611	+	0.725215i
$405$		−	1.19572e7i		−	0.179997i
$406$	1.88056e6	−	2.67342e7i	0.0281001	−	0.399475i
$407$	1.37707e7			0.204255
$408$	−1.18016e7	−	2.04411e7i	−0.173765	−	0.300970i
$409$	−8.98031e7	−	5.18478e7i	−1.31257	−	0.757811i	−0.330046	−	0.943965i	$-0.607064\pi$
$409$	−8.98031e7	−	5.18478e7i	−1.31257	−	0.757811i	−0.982521	+	0.186154i	$0.940398\pi$
$410$	8.83525e7	−	1.53031e8i	1.28194	−	2.22038i
$411$	−6.34517e7	+	3.66338e7i	−0.913940	+	0.527663i
$412$		−	7.15007e7i		−	1.02239i
$413$	4.21318e7	+	8.64738e7i	0.598081	+	1.22754i
$414$	3.86107e7			0.544135
$415$	−8.70129e7	−	1.50711e8i	−1.21742	−	2.10863i
$416$	−9.89844e6	−	5.71487e6i	−0.137495	−	0.0793827i
$417$	−1.28064e7	+	2.21813e7i	−0.176611	+	0.305899i
$418$	−1.27817e8	+	7.37954e7i	−1.75009	+	1.01042i
$419$			2.42723e7i			0.329965i	0.986296	+	0.164983i	$0.0527568\pi$
$419$			2.42723e7i			0.329965i	−0.986296	+	0.164983i	$0.947243\pi$
$420$	8.92204e7	−	4.34700e7i	1.20425	−	0.586734i
$421$	−8.03195e7			−1.07640			−0.538201	−	0.842816i	$-0.680896\pi$
$421$	−8.03195e7			−1.07640			−0.538201	+	0.842816i	$0.680896\pi$
$422$	2.29321e7	+	3.97195e7i	0.305145	+	0.528526i
$423$	−9.74824e6	−	5.62815e6i	−0.128797	−	0.0743609i
$424$	−2.20947e7	+	3.82692e7i	−0.289862	+	0.502055i
$425$	−9.64205e7	+	5.56684e7i	−1.25604	+	0.725174i
$426$		−	6.72376e7i		−	0.869727i
$427$	3.34872e7	+	2.35558e6i	0.430126	+	0.0302562i
$428$	−9.14527e7			−1.16645
$429$	1.87747e6	+	3.25186e6i	0.0237794	+	0.0411870i
$430$	2.47945e8	+	1.43151e8i	3.11854	+	1.80049i
$431$	2.93452e7	−	5.08273e7i	0.366526	−	0.634841i	−0.622494	−	0.782625i	$-0.713880\pi$
$431$	2.93452e7	−	5.08273e7i	0.366526	−	0.634841i	0.989020	+	0.147783i	$0.0472138\pi$
$432$	−5.11803e6	+	2.95490e6i	−0.0634822	+	0.0366514i
$433$			1.51707e8i			1.86871i	0.356344	+	0.934355i	$0.384023\pi$
$433$			1.51707e8i			1.86871i	−0.356344	+	0.934355i	$0.615977\pi$
$434$	−4.89110e7	+	7.24489e7i	−0.598326	+	0.886263i
$435$	−1.97684e7			−0.240161
$436$	−6.67167e7	−	1.15557e8i	−0.804962	−	1.39423i
$437$	−1.48975e8	−	8.60105e7i	−1.78512	−	1.03064i
$438$	−1.17442e7	+	2.03415e7i	−0.139766	+	0.242081i
$439$	1.05336e8	−	6.08155e7i	1.24504	−	0.718821i	0.274920	−	0.961467i	$-0.411349\pi$
$439$	1.05336e8	−	6.08155e7i	1.24504	−	0.718821i	0.970115	+	0.242646i	$0.0780152\pi$
$440$		−	6.12105e7i		−	0.718568i
$441$	−1.76196e7	+	2.25136e7i	−0.205438	+	0.262500i
$442$	1.50541e7			0.174336
$443$	−4.63310e7	−	8.02476e7i	−0.532918	−	0.923041i	−0.999261	−	0.0384371i	$-0.987762\pi$
$443$	−4.63310e7	−	8.02476e7i	−0.532918	−	0.923041i	0.466343	−	0.884604i	$-0.345571\pi$
$444$	1.94582e7	+	1.12342e7i	0.222307	+	0.128349i
$445$	1.82122e7	−	3.15444e7i	0.206672	−	0.357967i
$446$	1.54755e8	−	8.93480e7i	1.74438	−	1.00712i
$447$		−	7.21337e7i		−	0.807636i
$448$	−1.19005e8	−	8.03417e7i	−1.32352	−	0.893525i
$449$	−2.40772e7			−0.265991			−0.132996	−	0.991117i	$-0.542460\pi$
$449$	−2.40772e7			−0.265991			−0.132996	+	0.991117i	$0.542460\pi$
$450$	−3.84733e7	−	6.66377e7i	−0.422204	−	0.731278i
$451$	5.30465e7	+	3.06264e7i	0.578265	+	0.333862i
$452$	−8.14035e6	+	1.40995e7i	−0.0881511	+	0.152682i
$453$	6.06447e7	−	3.50133e7i	0.652377	−	0.376650i
$454$			3.78178e7i			0.404137i
$455$	−1.34051e6	+	1.90568e7i	−0.0142310	+	0.202309i
$456$	−7.26770e7			−0.766483
$457$	3.25397e7	+	5.63605e7i	0.340930	+	0.590509i	0.984606	−	0.174790i	$-0.0559247\pi$
$457$	3.25397e7	+	5.63605e7i	0.340930	+	0.590509i	−0.643675	+	0.765299i	$0.722591\pi$
$458$	6.76471e7	+	3.90561e7i	0.704130	+	0.406530i
$459$	8.30864e6	−	1.43910e7i	0.0859195	−	0.148817i
$460$	2.04718e8	−	1.18194e8i	2.10321	−	1.21429i
$461$			1.22022e8i			1.24548i	0.782429	+	0.622740i	$0.213980\pi$
$461$			1.22022e8i			1.24548i	−0.782429	+	0.622740i	$0.786020\pi$
$462$	2.55891e7	+	5.25206e7i	0.259495	+	0.532603i
$463$	2.62985e7			0.264965			0.132482	−	0.991185i	$-0.457705\pi$
$463$	2.62985e7			0.264965			0.132482	+	0.991185i	$0.457705\pi$
$464$	4.88521e6	+	8.46143e6i	0.0489023	+	0.0847012i
$465$	5.58394e7	+	3.22389e7i	0.555369	+	0.320643i
$466$	7.39061e7	−	1.28009e8i	0.730336	−	1.26498i
$467$	5.31512e7	−	3.06869e7i	0.521870	−	0.301302i	−0.215829	−	0.976431i	$-0.569245\pi$
$467$	5.31512e7	−	3.06869e7i	0.521870	−	0.301302i	0.737699	+	0.675129i	$0.235912\pi$
$468$			6.12657e6i			0.0597695i
$469$	−5.38246e7	+	2.62244e7i	−0.521750	+	0.254207i
$470$	−1.17031e8			−1.12722
$471$	−3.76073e7	−	6.51378e7i	−0.359923	−	0.623405i
$472$	8.38286e7	+	4.83985e7i	0.797198	+	0.460263i
$473$	−4.96218e7	+	8.59475e7i	−0.468909	+	0.812175i
$474$	−1.28661e8	+	7.42822e7i	−1.20812	+	0.697509i
$475$			3.42818e8i			3.19877i
$476$	1.37586e8	+	9.67818e6i	1.27571	+	0.0897373i
$477$	−3.11104e7			−0.286649
$478$	−2.67765e7	−	4.63783e7i	−0.245172	−	0.424650i
$479$	−1.67375e8	−	9.66342e7i	−1.52295	−	0.879274i	−0.999632	−	0.0271349i	$-0.991362\pi$
$479$	−1.67375e8	−	9.66342e7i	−1.52295	−	0.879274i	−0.523315	−	0.852139i	$-0.675305\pi$
$480$	−6.55869e7	+	1.13600e8i	−0.593053	+	1.02720i
$481$	−3.74548e6	+	2.16246e6i	−0.0336568	+	0.0194317i
$482$		−	1.97899e8i		−	1.76727i
$483$	−3.81006e7	+	5.64361e7i	−0.338135	+	0.500859i
$484$	−9.20854e7			−0.812184
$485$	−3.44417e7	−	5.96548e7i	−0.301898	−	0.522902i
$486$	9.94583e6	+	5.74223e6i	0.0866428	+	0.0500232i
$487$	−741867.	+	1.28495e6i	−0.00642302	+	0.0111250i	−0.869219	−	0.494427i	$-0.835378\pi$
$487$	−741867.	+	1.28495e6i	−0.00642302	+	0.0111250i	0.862796	+	0.505552i	$0.168711\pi$
$488$	2.92554e7	−	1.68906e7i	0.251737	−	0.145340i
$489$			5.29268e7i			0.452636i
$490$	−4.16108e7	+	2.94308e8i	−0.353686	+	2.50158i
$491$	1.33332e8			1.12639			0.563195	−	0.826324i	$-0.309572\pi$
$491$	1.33332e8			1.12639			0.563195	+	0.826324i	$0.309572\pi$
$492$	4.99702e7	+	8.65510e7i	0.419581	+	0.726736i
$493$	−2.37920e7	−	1.37363e7i	−0.198559	−	0.114638i
$494$	2.31766e7	−	4.01430e7i	0.192251	−	0.332988i
$495$	3.73202e7	−	2.15468e7i	0.307700	−	0.177651i
$496$		−	3.18678e7i		−	0.261161i
$497$	9.82790e7	+	6.63493e7i	0.800556	+	0.540464i
$498$	1.67145e8			1.35334
$499$	−7.54918e7	−	1.30756e8i	−0.607573	−	1.05235i	−0.991639	−	0.129042i	$-0.958810\pi$
$499$	−7.54918e7	−	1.30756e8i	−0.607573	−	1.05235i	0.384066	−	0.923306i	$-0.374523\pi$
$500$	−1.56808e8	−	9.05331e7i	−1.25446	−	0.724265i
$501$	1.59453e7	−	2.76181e7i	0.126800	−	0.219625i
$502$	−7.69050e7	+	4.44011e7i	−0.607915	+	0.350980i
$503$		−	9.92575e7i		−	0.779937i	−0.920828	−	0.389968i	$-0.872486\pi$
$503$		−	9.92575e7i		−	0.779937i	0.920828	−	0.389968i	$-0.127514\pi$
$504$	−2.01868e6	+	2.86977e7i	−0.0157680	+	0.224159i
$505$	−2.11279e8			−1.64052
$506$	6.95762e7	+	1.20510e8i	0.537043	+	0.930186i
$507$	6.41406e7	+	3.70316e7i	0.492163	+	0.284151i
$508$	−4.23661e7	+	7.33803e7i	−0.323167	+	0.559742i
$509$	1.07059e8	−	6.18103e7i	0.811835	−	0.468713i	−0.0357576	−	0.999360i	$-0.511384\pi$
$509$	1.07059e8	−	6.18103e7i	0.811835	−	0.468713i	0.847593	+	0.530647i	$0.178051\pi$
$510$		−	1.72769e8i		−	1.30243i
$511$	−1.81435e7	−	3.72389e7i	−0.135975	−	0.279083i
$512$	9.92957e7			0.739811
$513$	−2.55832e7	−	4.43114e7i	−0.189497	−	0.328218i
$514$	7.79430e7	+	4.50004e7i	0.573968	+	0.331381i
$515$	7.89762e7	−	1.36791e8i	0.578195	−	1.00146i
$516$	−1.40232e8	+	8.09632e7i	−1.02070	+	0.589303i
$517$		−	4.05675e7i		−	0.293567i
$518$	−6.04929e7	+	2.94734e7i	−0.435226	+	0.212051i
$519$	−4.90965e6			−0.0351195
$520$	9.61205e6	+	1.66486e7i	0.0683606	+	0.118404i
$521$	1.41733e8	+	8.18296e7i	1.00221	+	0.578625i	0.908901	−	0.417012i	$-0.136923\pi$
$521$	1.41733e8	+	8.18296e7i	1.00221	+	0.578625i	0.0933071	+	0.995637i	$0.470256\pi$
$522$	9.49339e6	−	1.64430e7i	0.0667436	−	0.115603i
$523$	2.21384e8	−	1.27816e8i	1.54754	−	0.893471i	0.549208	−	0.835686i	$-0.314930\pi$
$523$	2.21384e8	−	1.27816e8i	1.54754	−	0.893471i	0.998329	−	0.0577847i	$-0.0184037\pi$
$524$			8.86584e7i			0.616206i
$525$	1.35367e8	+	9.52211e6i	0.935483	+	0.0658044i
$526$	−2.06623e8			−1.41978
$527$	4.48033e7	+	7.76016e7i	0.306111	+	0.530199i
$528$	−1.84453e7	−	1.06494e7i	−0.125310	−	0.0723475i
$529$	−7.07498e6	+	1.22542e7i	−0.0477924	+	0.0827788i
$530$	−2.80119e8	+	1.61727e8i	−1.88154	+	1.08631i
$531$			6.81474e7i			0.455161i
$532$	2.37629e8	−	3.51985e8i	1.57821	−	2.33770i
$533$	−1.92374e7			−0.127047
$534$	1.74921e7	+	3.02973e7i	0.114873	+	0.198966i
$535$	−1.74962e8	−	1.01014e8i	−1.14257	−	0.659661i
$536$	−3.01251e7	+	5.21781e7i	−0.195629	+	0.338840i
$537$	5.43250e7	−	3.13645e7i	0.350814	−	0.202542i
$538$		−	6.82152e7i		−	0.438061i
$539$	−1.02019e8	−	1.44239e7i	−0.651498	−	0.0921122i
$540$	7.03118e7			0.446526
$541$	1.21035e8	+	2.09639e8i	0.764398	+	1.32398i	0.940564	+	0.339616i	$0.110297\pi$
$541$	1.21035e8	+	2.09639e8i	0.764398	+	1.32398i	−0.176166	+	0.984361i	$0.556369\pi$
$542$	2.01613e8	+	1.16401e8i	1.26625	+	0.731072i
$543$	−1.19891e7	+	2.07658e7i	−0.0748838	+	0.129703i
$544$	−1.57873e8	+	9.11480e7i	−0.980643	+	0.566175i
$545$		−	2.94768e8i		−	1.82092i
$546$	−1.52074e7	−	1.02667e7i	−0.0934279	−	0.0630742i
$547$	−3.05715e7			−0.186790			−0.0933952	−	0.995629i	$-0.529772\pi$
$547$	−3.05715e7			−0.186790			−0.0933952	+	0.995629i	$0.529772\pi$
$548$	−2.15417e8	−	3.73114e8i	−1.30900	−	2.26725i
$549$	2.05965e7	+	1.18914e7i	0.124473	+	0.0718648i
$550$	1.38657e8	−	2.40161e8i	0.833402	−	1.44349i
$551$	−7.32581e7	+	4.22956e7i	−0.437926	+	0.252837i
$552$			6.85218e7i			0.407391i
$553$	1.83848e7	−	2.61360e8i	0.108713	−	1.54548i
$554$	−9.52587e7			−0.560242
$555$	2.48175e7	+	4.29852e7i	0.145171	+	0.251443i
$556$	−1.30432e8	−	7.53050e7i	−0.758857	−	0.438126i
$557$	−1.16542e8	+	2.01856e8i	−0.674396	+	1.16809i	0.302249	+	0.953229i	$0.402263\pi$
$557$	−1.16542e8	+	2.01856e8i	−0.674396	+	1.16809i	−0.976645	+	0.214860i	$0.931071\pi$
$558$	−5.36317e7	+	3.09643e7i	−0.308687	+	0.178221i
$559$		−	3.11690e7i		−	0.178438i
$560$	−4.74622e7	−	9.74142e7i	−0.270261	−	0.554700i
$561$	5.98884e7			0.339199
$562$	1.78584e8	+	3.09317e8i	1.00608	+	1.74259i
$563$	1.95271e8	+	1.12740e8i	1.09424	+	0.631758i	0.934702	−	0.355434i	$-0.115667\pi$
$563$	1.95271e8	+	1.12740e8i	1.09424	+	0.631758i	0.159536	+	0.987192i	$0.449000\pi$
$564$	3.30951e7	−	5.73224e7i	0.184470	−	0.319512i
$565$	−3.11472e7	+	1.79829e7i	−0.172693	+	0.0997042i
$566$			2.65638e8i			1.46501i
$567$	−1.82077e7	+	8.87115e6i	−0.0998862	+	0.0486666i
$568$	1.19325e8			0.651160
$569$	−1.07390e8	−	1.86004e8i	−0.582943	−	1.00969i	−0.995128	−	0.0985864i	$-0.968568\pi$
$569$	−1.07390e8	−	1.86004e8i	−0.582943	−	1.00969i	0.412186	−	0.911100i	$-0.364765\pi$
$570$	−4.60703e8	−	2.65987e8i	−2.48769	−	1.43627i
$571$	−1.71362e8	+	2.96807e8i	−0.920460	+	1.59428i	−0.121757	+	0.992560i	$0.538853\pi$
$571$	−1.71362e8	+	2.96807e8i	−0.920460	+	1.59428i	−0.798704	+	0.601724i	$0.794481\pi$
$572$	−1.91219e7	+	1.10400e7i	−0.102175	+	0.0589905i
$573$		−	6.66766e7i		−	0.354413i
$574$	−2.98575e8	−	2.10026e7i	−1.57877	−	0.111055i
$575$	3.23217e8			1.70017
$576$	−5.08622e7	−	8.80959e7i	−0.266151	−	0.460986i
$577$	2.42646e8	+	1.40092e8i	1.26312	+	0.729263i	0.973677	−	0.227931i	$-0.0731962\pi$
$577$	2.42646e8	+	1.40092e8i	1.26312	+	0.729263i	0.289444	+	0.957195i	$0.406530\pi$
$578$	−3.05259e7	+	5.28724e7i	−0.158083	+	0.273807i
$579$	8.70243e7	−	5.02435e7i	0.448337	−	0.258848i
$580$		−	1.16244e8i		−	0.595779i
$581$	−1.64937e8	+	2.44311e8i	−0.840989	+	1.24570i
$582$	6.61600e7			0.335604
$583$	−5.60607e7	−	9.71000e7i	−0.282913	−	0.490020i
$584$	−3.60997e7	−	2.08422e7i	−0.181245	−	0.104642i
$585$	−6.76711e6	+	1.17210e7i	−0.0338015	+	0.0585458i
$586$	−1.85956e8	+	1.07362e8i	−0.924098	+	0.533528i
$587$		−	2.73172e8i		−	1.35059i	−0.737549	−	0.675293i	$-0.764017\pi$
$587$		−	2.73172e8i		−	1.35059i	0.737549	−	0.675293i	$-0.235983\pi$
$588$	−1.32387e8	−	1.03608e8i	−0.651196	−	0.509639i
$589$	2.75908e8			1.35026
$590$	3.54262e8	+	6.13600e8i	1.72492	+	2.98765i
$591$	−3.68840e7	−	2.12950e7i	−0.178680	−	0.103161i
$592$	1.22659e7	−	2.12452e7i	0.0591201	−	0.102399i
$593$	−3.17713e8	+	1.83432e8i	−1.52360	+	0.879651i	−0.523991	+	0.851724i	$0.675557\pi$
$593$	−3.17713e8	+	1.83432e8i	−1.52360	+	0.879651i	−0.999610	+	0.0279272i	$0.991109\pi$
$594$			4.13898e7i			0.197485i
$595$	2.52531e8	+	1.70487e8i	1.19885	+	0.809355i
$596$	4.24167e8			2.00354
$597$	4.65507e6	+	8.06283e6i	0.0218778	+	0.0378935i
$598$	−3.78479e7	−	2.18515e7i	−0.176986	−	0.102183i
$599$	8.45253e7	−	1.46402e8i	0.393284	−	0.681188i	−0.599596	−	0.800303i	$-0.704672\pi$
$599$	8.45253e7	−	1.46402e8i	0.393284	−	0.681188i	0.992881	+	0.119114i	$0.0380055\pi$
$600$	1.18261e8	−	6.82779e7i	0.547504	−	0.316102i
$601$			1.61411e8i			0.743551i	0.928323	+	0.371775i	$0.121251\pi$
$601$			1.61411e8i			0.743551i	−0.928323	+	0.371775i	$0.878749\pi$
$602$	3.40290e7	−	4.83760e8i	0.155977	−	2.21738i
$603$	−4.24175e7			−0.193461
$604$	2.05888e8	+	3.56608e8i	0.934373	+	1.61838i
$605$	−1.76172e8	−	1.01713e8i	−0.795556	−	0.459315i
$606$	1.01463e8	−	1.75739e8i	0.455921	−	0.789678i
$607$	1.67933e8	−	9.69564e7i	0.750881	−	0.433521i	−0.0751313	−	0.997174i	$-0.523938\pi$
$607$	1.67933e8	−	9.69564e7i	0.750881	−	0.433521i	0.826012	+	0.563652i	$0.190604\pi$
$608$			5.61309e8i			2.49742i
$609$	1.46663e7	+	3.01020e7i	0.0649335	+	0.133273i
$610$	2.47269e8			1.08938
$611$	6.37043e6	+	1.10339e7i	0.0279283	+	0.0483733i
$612$	8.46231e7	+	4.88572e7i	0.369177	+	0.213144i
$613$	5.21774e7	−	9.03739e7i	0.226517	−	0.392339i	−0.730256	−	0.683173i	$-0.760599\pi$
$613$	5.21774e7	−	9.03739e7i	0.226517	−	0.392339i	0.956773	+	0.290834i	$0.0939328\pi$
$614$	4.44359e8	−	2.56551e8i	1.91968	−	1.10833i
$615$			2.20779e8i			0.949143i
$616$	−9.32074e7	+	4.54125e7i	−0.398757	+	0.194282i
$617$	−3.99769e8			−1.70198			−0.850989	−	0.525183i	$-0.823997\pi$
$617$	−3.99769e8			−1.70198			−0.850989	+	0.525183i	$0.823997\pi$
$618$	7.58537e7	+	1.31382e8i	0.321374	+	0.556637i
$619$	−2.11757e8	−	1.22258e8i	−0.892822	−	0.515471i	−0.0179577	−	0.999839i	$-0.505716\pi$
$619$	−2.11757e8	−	1.22258e8i	−0.892822	−	0.515471i	−0.874865	+	0.484368i	$0.839050\pi$
$620$	−1.89574e8	+	3.28352e8i	−0.795433	+	1.37773i
$621$	−4.17779e7	+	2.41205e7i	−0.174450	+	0.100719i
$622$		−	1.42350e8i		−	0.591544i
$623$	−6.15456e7	−	4.32929e6i	−0.254526	−	0.0179041i
$624$	6.68922e6			0.0275310
$625$	−1.71720e6	−	2.97427e6i	−0.00703363	−	0.0121826i
$626$	1.16057e7	+	6.70056e6i	0.0473095	+	0.0273142i
$627$	9.22014e7	−	1.59698e8i	0.374055	−	0.647881i
$628$	3.83029e8	−	2.21142e8i	1.54651	−	0.892877i
$629$			6.89792e7i			0.277183i
$630$	−1.17826e8	+	1.74528e8i	−0.471215	+	0.697982i
$631$	−2.46592e8			−0.981500			−0.490750	−	0.871301i	$-0.663277\pi$
$631$	−2.46592e8			−0.981500			−0.490750	+	0.871301i	$0.663277\pi$
$632$	−1.31827e8	−	2.28332e8i	−0.522221	−	0.904514i
$633$	−4.96263e7	−	2.86517e7i	−0.195659	−	0.112964i
$634$	1.23515e8	−	2.13935e8i	0.484677	−	0.839486i
$635$	−1.62105e8	+	9.35911e7i	−0.633102	+	0.365522i
$636$		−	1.82938e8i		−	0.711103i
$637$	3.00129e7	−	1.20971e7i	0.116116	−	0.0468019i
$638$	6.84281e7			0.263495
$639$	4.20040e7	+	7.27530e7i	0.160986	+	0.278836i
$640$	−4.49533e8	−	2.59538e8i	−1.71483	−	0.990058i
$641$	−1.80422e8	+	3.12501e8i	−0.685040	+	1.18652i	0.288384	+	0.957515i	$0.406882\pi$
$641$	−1.80422e8	+	3.12501e8i	−0.685040	+	1.18652i	−0.973424	+	0.229010i	$0.926451\pi$
$642$	1.68044e8	−	9.70204e7i	0.635066	−	0.366655i
$643$		−	9.49305e7i		−	0.357086i	−0.983932	−	0.178543i	$-0.942862\pi$
$643$		−	9.49305e7i		−	0.357086i	0.983932	−	0.178543i	$-0.0571384\pi$
$644$	−3.31860e8	−	2.24042e8i	−1.24250	−	0.838827i
$645$	−3.57712e8			−1.33307
$646$	−3.69650e8	−	6.40252e8i	−1.37118	−	2.37495i
$647$	−1.29149e8	−	7.45642e7i	−0.476846	−	0.275307i	0.242255	−	0.970213i	$-0.422113\pi$
$647$	−1.29149e8	−	7.45642e7i	−0.476846	−	0.275307i	−0.719101	+	0.694905i	$0.755446\pi$
$648$	−1.01906e7	+	1.76507e7i	−0.0374521	+	0.0648690i
$649$	−2.12698e8	+	1.22801e8i	−0.778088	+	0.449229i
$650$			8.70949e7i			0.317141i
$651$	7.66363e6	−	1.08947e8i	0.0277774	−	0.394886i
$652$	−3.11225e8			−1.12288
$653$	2.54667e6	+	4.41096e6i	0.00914604	+	0.0158414i	0.870562	−	0.492058i	$-0.163755\pi$
$653$	2.54667e6	+	4.41096e6i	0.00914604	+	0.0158414i	−0.861416	+	0.507900i	$0.830422\pi$
$654$	2.45184e8	+	1.41557e8i	0.876514	+	0.506055i
$655$	−9.79278e7	+	1.69616e8i	−0.348483	+	0.603591i
$656$	9.44997e7	−	5.45594e7i	0.334749	−	0.193267i
$657$		−	2.93468e7i		−	0.103482i
$658$	8.68263e7	+	1.78208e8i	0.304771	+	0.625530i
$659$	5.76822e6			0.0201551			0.0100776	−	0.999949i	$-0.496792\pi$
$659$	5.76822e6			0.0201551			0.0100776	+	0.999949i	$0.496792\pi$
$660$	1.26701e8	+	2.19453e8i	0.440707	+	0.763326i
$661$	1.29229e7	+	7.46102e6i	0.0447460	+	0.0258341i	0.522206	−	0.852819i	$-0.325109\pi$
$661$	1.29229e7	+	7.46102e6i	0.0447460	+	0.0258341i	−0.477460	+	0.878653i	$0.658442\pi$
$662$	1.19352e8	−	2.06724e8i	0.411392	−	0.712552i
$663$	−1.62890e7	+	9.40444e6i	−0.0558924	+	0.0322695i
$664$			2.96630e8i			1.01324i
$665$	8.43402e8	−	4.10922e8i	2.86794	−	1.39732i
$666$	−4.76726e7			−0.161379
$667$	3.98774e7	+	6.90696e7i	0.134384	+	0.232761i
$668$	1.62402e8	+	9.37631e7i	0.544833	+	0.314559i
$669$	−1.11633e8	+	1.93354e8i	−0.372833	+	0.645766i
$670$	−3.81928e8	+	2.20506e8i	−1.26986	+	0.733157i
$671$			8.57129e7i			0.283713i
$672$	2.21642e8	+	1.55909e7i	0.730372	+	0.0513764i
$673$	2.64968e8			0.869257			0.434629	−	0.900610i	$-0.356880\pi$
$673$	2.64968e8			0.869257			0.434629	+	0.900610i	$0.356880\pi$
$674$	−3.82396e8	−	6.62330e8i	−1.24892	−	2.16319i
$675$	8.32584e7	+	4.80693e7i	0.270718	+	0.156299i
$676$	−2.17756e8	+	3.77165e8i	−0.704905	+	1.22093i
$677$	2.64867e8	−	1.52921e8i	0.853615	−	0.492835i	−0.00825369	−	0.999966i	$-0.502627\pi$
$677$	2.64867e8	−	1.52921e8i	0.853615	−	0.492835i	0.861869	+	0.507131i	$0.169294\pi$
$678$		−	3.45438e7i		−	0.110836i
$679$	−6.52860e7	+	9.67041e7i	−0.208550	+	0.308912i
$680$	3.06610e8			0.975125
$681$	−2.36252e7	−	4.09200e7i	−0.0748055	−	0.129567i
$682$	−1.93288e8	−	1.11595e8i	−0.609328	−	0.351796i
$683$	−7.48455e7	+	1.29636e8i	−0.234911	+	0.406878i	−0.959247	−	0.282570i	$-0.908813\pi$
$683$	−7.48455e7	+	1.29636e8i	−0.234911	+	0.406878i	0.724336	+	0.689447i	$0.242147\pi$
$684$	2.60563e8	−	1.50436e8i	0.814227	−	0.470094i
$685$		−	9.51758e8i		−	2.96111i
$686$	4.79025e8	−	1.54987e8i	1.48384	−	0.480091i
$687$	−9.75949e7			−0.300993
$688$	8.83987e7	+	1.53111e8i	0.271444	+	0.470155i
$689$	3.04957e7	+	1.76067e7i	0.0932356	+	0.0538296i
$690$	−2.50779e8	+	4.34363e8i	−0.763387	+	1.32222i
$691$	2.20972e8	−	1.27578e8i	0.669736	−	0.386672i	−0.126241	−	0.992000i	$-0.540291\pi$
$691$	2.20972e8	−	1.27578e8i	0.669736	−	0.386672i	0.795977	+	0.605327i	$0.206958\pi$
$692$		−	2.88701e7i		−	0.0871225i
$693$	−6.04982e7	−	4.08430e7i	−0.181779	−	0.122721i
$694$	9.67949e8			2.89584
$695$	−1.66356e8	−	2.88138e8i	−0.495548	−	0.858313i
$696$	2.91812e7	+	1.68478e7i	0.0865516	+	0.0499706i
$697$	−1.53411e8	+	2.65716e8i	−0.453063	+	0.784729i
$698$	−3.59205e8	+	2.07387e8i	−1.05627	+	0.609840i
$699$			1.84679e8i			0.540738i
$700$	−5.59927e7	+	7.95998e8i	−0.163244	+	2.32069i
$701$	−2.47105e8			−0.717343			−0.358672	−	0.933464i	$-0.616770\pi$
$701$	−2.47105e8			−0.717343			−0.358672	+	0.933464i	$0.616770\pi$
$702$	−6.49956e6	−	1.12576e7i	−0.0187876	−	0.0325412i
$703$	1.83939e8	+	1.06197e8i	0.529429	+	0.305666i
$704$	1.83307e8	−	3.17496e8i	0.525364	−	0.909956i
$705$	1.26631e8	−	7.31105e7i	0.361387	−	0.208647i
$706$			2.42584e8i			0.689364i
$707$	1.56750e8	+	3.21722e8i	0.443556	+	0.910381i
$708$	−4.00726e8			−1.12914
$709$	5.21037e7	+	9.02462e7i	0.146194	+	0.253215i	0.929818	−	0.368020i	$-0.119964\pi$
$709$	5.21037e7	+	9.02462e7i	0.146194	+	0.253215i	−0.783624	+	0.621236i	$0.786631\pi$
$710$	7.56409e8	+	4.36713e8i	2.11340	+	1.22017i
$711$	9.28096e7	−	1.60751e8i	0.258217	−	0.447244i
$712$	−5.37680e7	+	3.10430e7i	−0.148965	+	0.0860050i
$713$		−	2.60133e8i		−	0.717675i
$714$	−2.63082e8	+	1.28179e8i	−0.722763	+	0.352145i
$715$	−4.87771e7			−0.133444
$716$	1.84432e8	+	3.19446e8i	0.502456	+	0.870279i
$717$	5.79460e7	+	3.34551e7i	0.157205	+	0.0907622i
$718$	−1.58748e8	+	2.74960e8i	−0.428879	+	0.742841i
$719$	−4.11126e8	+	2.37363e8i	−1.10608	+	0.638598i	−0.937812	−	0.347143i	$-0.887152\pi$
$719$	−4.11126e8	+	2.37363e8i	−1.10608	+	0.638598i	−0.168271	+	0.985741i	$0.553818\pi$
$720$		−	7.67691e7i		−	0.205679i
$721$	−2.66889e8	−	1.87737e7i	−0.712074	−	0.0500893i
$722$	−1.68941e9			−4.48873
$723$	1.23630e8	+	2.14133e8i	0.327121	+	0.566589i
$724$	−1.22109e8	−	7.04995e7i	−0.321759	−	0.185768i
$725$	7.94709e7	−	1.37648e8i	0.208542	−	0.361206i
$726$	1.69207e8	−	9.76916e7i	0.442189	−	0.255298i
$727$		−	1.04048e8i		−	0.270790i	−0.990792	−	0.135395i	$-0.956770\pi$
$727$		−	1.04048e8i		−	0.270790i	0.990792	−	0.135395i	$-0.0432303\pi$
$728$	1.82201e7	−	2.69883e7i	0.0472233	−	0.0699490i
$729$	−1.43489e7			−0.0370370
$730$	−1.52559e8	−	2.64239e8i	−0.392164	−	0.679249i
$731$	−4.30521e8	−	2.48561e8i	−1.10215	−	0.636329i
$732$	−6.99248e7	+	1.21113e8i	−0.178278	+	0.308787i
$733$	5.79355e8	−	3.34491e8i	1.47107	−	0.849322i	0.471597	−	0.881814i	$-0.343678\pi$
$733$	5.79355e8	−	3.34491e8i	1.47107	−	0.849322i	0.999472	+	0.0324917i	$0.0103443\pi$
$734$			1.01239e8i			0.256010i
$735$	−1.38833e8	−	3.44445e8i	−0.349648	−	0.867476i
$736$	5.29216e8			1.32739
$737$	−7.64361e7	−	1.32391e8i	−0.190940	−	0.330717i
$738$	−1.83641e8	−	1.06025e8i	−0.456877	−	0.263778i
$739$	1.54148e8	−	2.66992e8i	0.381948	−	0.661554i	−0.609393	−	0.792869i	$-0.708587\pi$
$739$	1.54148e8	−	2.66992e8i	0.381948	−	0.661554i	0.991341	+	0.131315i	$0.0419200\pi$
$740$	−2.52765e8	+	1.45934e8i	−0.623767	+	0.360132i
$741$			5.79145e7i			0.142342i
$742$	4.54089e8	+	3.06561e8i	1.11155	+	0.750420i
$743$	1.83763e8			0.448014			0.224007	−	0.974588i	$-0.428086\pi$
$743$	1.83763e8			0.448014			0.224007	+	0.974588i	$0.428086\pi$
$744$	−5.49518e7	−	9.51793e7i	−0.133433	−	0.231113i
$745$	8.11490e8	+	4.68514e8i	1.96252	+	1.13306i
$746$	4.49560e8	−	7.78661e8i	1.08286	−	1.87556i
$747$	−1.80856e8	+	1.04417e8i	−0.433882	+	0.250502i
$748$			3.52161e8i			0.841466i
$749$	−2.40125e7	+	3.41364e8i	−0.0571467	+	0.812404i
$750$	3.84179e8			0.910647
$751$	−1.22666e8	−	2.12463e8i	−0.289603	−	0.501608i	0.684112	−	0.729377i	$-0.260190\pi$
$751$	−1.22666e8	−	2.12463e8i	−0.289603	−	0.501608i	−0.973715	+	0.227770i	$0.926857\pi$
$752$	−6.25868e7	−	3.61345e7i	−0.147173	−	0.0849706i
$753$	5.54756e7	−	9.60865e7i	0.129932	−	0.225049i
$754$	−1.86117e7	+	1.07454e7i	−0.0434181	+	0.0250675i
$755$			9.09655e8i			2.11366i
$756$	−5.21649e7	−	1.07066e8i	−0.120729	−	0.247792i
$757$	−8.44770e8			−1.94738			−0.973690	−	0.227876i	$-0.926822\pi$
$757$	−8.44770e8			−1.94738			−0.973690	+	0.227876i	$0.926822\pi$
$758$	−2.83040e8	−	4.90240e8i	−0.649891	−	1.12564i
$759$	−1.50567e8	−	8.69299e7i	−0.344353	−	0.198812i
$760$	4.72043e8	−	8.17602e8i	1.07533	−	1.86252i
$761$	4.91638e8	−	2.83847e8i	1.11556	−	0.644066i	0.175293	−	0.984516i	$-0.443913\pi$
$761$	4.91638e8	−	2.83847e8i	1.11556	−	0.644066i	0.940263	+	0.340450i	$0.110579\pi$
$762$		−	1.79782e8i		−	0.406331i
$763$	−4.48854e8	+	2.18691e8i	−1.01049	+	0.492331i
$764$	3.92077e8			0.879208
$765$	1.07930e8	+	1.86941e8i	0.241079	+	0.417562i
$766$	−8.18291e8	−	4.72440e8i	−1.82063	−	1.05114i
$767$	3.85676e7	−	6.68010e7i	0.0854744	−	0.148046i
$768$	7.00729e7	−	4.04566e7i	0.154692	−	0.0893112i
$769$			2.83103e6i			0.00622536i	0.999995	+	0.00311268i	$0.000990799\pi$
$769$			2.83103e6i			0.00622536i	−0.999995	+	0.00311268i	$0.999009\pi$
$770$	−7.57049e8	−	5.32529e7i	−1.65826	−	0.116646i
$771$	−1.12449e8			−0.245353
$772$	2.95446e8	+	5.11728e8i	0.642135	+	1.11221i
$773$	3.83914e8	+	2.21653e8i	0.831181	+	0.479883i	0.854257	−	0.519851i	$-0.174013\pi$
$773$	3.83914e8	+	2.21653e8i	0.831181	+	0.479883i	−0.0230756	+	0.999734i	$0.507346\pi$
$774$	1.71785e8	−	2.97540e8i	0.370477	−	0.641685i
$775$	−4.48961e8	+	2.59208e8i	−0.964503	+	0.556856i
$776$			1.17413e8i			0.251265i
$777$	4.70428e7	−	6.96816e7i	0.100284	−	0.148544i
$778$	1.10161e8			0.233931
$779$	4.72369e8	+	8.18168e8i	0.999239	+	1.73073i
$780$	−6.89227e7	−	3.97925e7i	−0.145237	−	0.0838528i
$781$	−1.51382e8	+	2.62201e8i	−0.317775	+	0.550403i
$782$	−6.03646e8	+	3.48515e8i	−1.26230	+	0.728789i
$783$			2.37224e7i			0.0494168i
$784$	−1.13124e8	+	1.44545e8i	−0.234750	+	0.299954i
$785$	9.77049e8			2.01980
$786$	−9.40560e7	−	1.62910e8i	−0.193695	−	0.335490i
$787$	6.26836e7	+	3.61904e7i	0.128597	+	0.0742454i	0.562918	−	0.826512i	$-0.309679\pi$
$787$	6.26836e7	+	3.61904e7i	0.128597	+	0.0742454i	−0.434322	+	0.900758i	$0.643012\pi$
$788$	1.25220e8	−	2.16888e8i	0.255916	−	0.443259i
$789$	2.23572e8	−	1.29080e8i	0.455184	−	0.262801i
$790$		−	1.92987e9i		−	3.91424i
$791$	5.04915e7	+	3.40874e7i	0.102021	+	0.0688754i
$792$	−7.34539e7			−0.147856
$793$	−1.34597e7	−	2.33129e7i	−0.0269909	−	0.0467495i
$794$	4.30616e8	+	2.48616e8i	0.860258	+	0.496670i
$795$	2.02064e8	−	3.49986e8i	0.402150	−	0.696545i
$796$	−4.74117e7	+	2.73732e7i	−0.0940040	+	0.0542733i
$797$		−	8.26919e8i		−	1.63338i	−0.577075	−	0.816691i	$-0.695806\pi$
$797$		−	8.26919e8i		−	1.63338i	0.577075	−	0.816691i	$-0.304194\pi$
$798$	−6.32288e7	+	8.98867e8i	−0.124425	+	1.76883i
$799$	2.03207e8			0.398382
$800$	−5.27333e8	−	9.13367e8i	−1.02995	−	1.78392i
$801$	−3.78540e7	−	2.18550e7i	−0.0736570	−	0.0425259i
$802$	2.06570e7	−	3.57789e7i	0.0400446	−	0.0693592i
$803$	9.15956e7	−	5.28827e7i	0.176900	−	0.102133i
$804$		−	2.49427e8i		−	0.479927i
$805$	−3.87428e8	−	7.95181e8i	−0.742683	−	1.52433i
$806$	7.00961e7			0.133872
$807$	4.26147e7	+	7.38109e7i	0.0810847	+	0.140443i
$808$	3.11881e8	+	1.80065e8i	0.591228	+	0.341346i
$809$	1.39404e8	−	2.41454e8i	0.263287	−	0.456026i	−0.703827	−	0.710372i	$-0.748527\pi$
$809$	1.39404e8	−	2.41454e8i	0.263287	−	0.456026i	0.967113	+	0.254346i	$0.0818602\pi$
$810$	−1.29198e8	+	7.45924e7i	−0.243109	+	0.140359i
$811$			8.06633e8i			1.51222i	0.654447	+	0.756108i	$0.272901\pi$
$811$			8.06633e8i			1.51222i	−0.654447	+	0.756108i	$0.727099\pi$
$812$	−1.77008e8	+	8.62420e7i	−0.330617	+	0.161083i
$813$	−2.90868e8			−0.541284
$814$	−8.59057e7	−	1.48793e8i	−0.159275	−	0.275873i
$815$	−5.95416e8	−	3.43764e8i	−1.09989	−	0.635020i
$816$	5.33441e7	−	9.23947e7i	0.0981784	−	0.170050i
$817$	−1.32562e9	+	7.65347e8i	−2.43082	+	1.40343i
$818$			1.29377e9i			2.36372i
$819$	2.28685e7	+	1.60863e6i	0.0416281	+	0.00292823i
$820$	−1.29824e9			−2.35458
$821$	5.29504e8	+	9.17127e8i	0.956840	+	1.65730i	0.730100	+	0.683341i	$0.239474\pi$
$821$	5.29504e8	+	9.17127e8i	0.956840	+	1.65730i	0.226741	+	0.973955i	$0.427193\pi$
$822$	7.91658e8	+	4.57064e8i	1.42535	+	0.822928i
$823$	5.41564e8	−	9.38017e8i	0.971517	−	1.68272i	0.280538	−	0.959843i	$-0.409487\pi$
$823$	5.41564e8	−	9.38017e8i	0.971517	−	1.68272i	0.690979	−	0.722875i	$-0.257180\pi$
$824$	−2.33162e8	+	1.34616e8i	−0.416751	+	0.240611i
$825$			3.46482e8i			0.617048i
$826$	6.71521e8	−	9.94683e8i	1.19157	−	1.76500i
$827$	−1.33362e8			−0.235785			−0.117892	−	0.993026i	$-0.537614\pi$
$827$	−1.33362e8			−0.235785			−0.117892	+	0.993026i	$0.537614\pi$
$828$	−1.41835e8	−	2.45666e8i	−0.249858	−	0.432767i
$829$	2.16051e8	+	1.24737e8i	0.379221	+	0.218944i	0.677479	−	0.735542i	$-0.263072\pi$
$829$	2.16051e8	+	1.24737e8i	0.379221	+	0.218944i	−0.298258	+	0.954485i	$0.596406\pi$
$830$	−1.08562e9	+	1.88035e9i	−1.89865	+	3.28855i
$831$	1.03073e8	−	5.95090e7i	0.179614	−	0.103700i
$832$			1.15140e8i			0.199921i
$833$	7.22511e7	−	5.11023e8i	0.125000	−	0.884109i
$834$	3.19558e8			0.550874
$835$	2.07132e8	+	3.58764e8i	0.355786	+	0.616239i
$836$	9.39067e8	+	5.42171e8i	1.60723	+	0.927934i
$837$	3.86874e7	−	6.70085e7i	0.0659770	−	0.114276i
$838$	2.62262e8	−	1.51417e8i	0.445660	−	0.257302i
$839$			4.92485e8i			0.833887i	0.908932	+	0.416943i	$0.136899\pi$
$839$			4.92485e8i			0.833887i	−0.908932	+	0.416943i	$0.863101\pi$
$840$	−3.09732e8	−	2.09104e8i	−0.522575	−	0.352796i
$841$	−5.55604e8			−0.934066
$842$	5.01056e8	+	8.67854e8i	0.839363	+	1.45382i
$843$	−3.86467e8	−	2.23127e8i	−0.645103	−	0.372450i
$844$	1.68480e8	−	2.91817e8i	0.280235	−	0.485381i
$845$	−8.33196e8	+	4.81046e8i	−1.38095	+	0.797291i
$846$			1.40440e8i			0.231942i
$847$	−2.41786e7	+	3.43725e8i	−0.0397906	+	0.565667i
$848$	−1.99739e8			−0.327548
$849$	−1.65947e8	−	2.87428e8i	−0.271173	−	0.469685i
$850$	1.20300e9	+	6.94550e8i	1.95888	+	1.13096i
$851$	1.00125e8	−	1.73422e8i	0.162463	−	0.281395i
$852$	−4.27808e8	+	2.46995e8i	−0.691720	+	0.399365i
$853$		−	6.41660e8i		−	1.03385i	−0.856031	−	0.516925i	$-0.827077\pi$
$853$		−	6.41660e8i		−	1.03385i	0.856031	−	0.516925i	$-0.172923\pi$
$854$	−1.83451e8	−	3.76525e8i	−0.294541	−	0.604533i
$855$	6.64659e8			1.06341
$856$	1.72180e8	+	2.98225e8i	0.274513	+	0.475470i
$857$	6.22262e8	+	3.59263e8i	0.988623	+	0.570782i	0.904863	−	0.425704i	$-0.139973\pi$
$857$	6.22262e8	+	3.59263e8i	0.988623	+	0.570782i	0.0837609	+	0.996486i	$0.473307\pi$
$858$	2.34243e7	−	4.05721e7i	0.0370856	−	0.0642341i
$859$	6.76979e8	−	3.90854e8i	1.06806	−	0.616645i	0.140409	−	0.990094i	$-0.455158\pi$
$859$	6.76979e8	−	3.90854e8i	1.06806	−	0.616645i	0.927651	+	0.373449i	$0.121825\pi$
$860$		−	2.10345e9i		−	3.30702i
$861$	3.36188e8	−	1.63797e8i	0.526711	−	0.256624i
$862$	−7.32253e8			−1.14325
$863$	−5.41290e8	−	9.37542e8i	−0.842166	−	1.45867i	−0.888060	−	0.459729i	$-0.847947\pi$
$863$	−5.41290e8	−	9.37542e8i	−0.842166	−	1.45867i	0.0458932	−	0.998946i	$-0.485387\pi$
$864$	1.36322e8	+	7.87057e7i	0.211361	+	0.122029i
$865$	3.18885e7	−	5.52325e7i	0.0492704	−	0.0853388i
$866$	1.63920e9	−	9.46391e8i	2.52393	−	1.45719i
$867$		−	7.62793e7i		−	0.117044i
$868$	6.40639e8	+	4.50643e7i	0.979613	+	0.0689087i
$869$	6.68969e8			1.01940
$870$	1.23321e8	+	2.13597e8i	0.187274	+	0.324368i
$871$	4.15795e7	+	2.40059e7i	0.0629252	+	0.0363299i
$872$	−2.51219e8	+	4.35124e8i	−0.378881	+	0.656241i
$873$	−7.15871e7	+	4.13308e7i	−0.107595	+	0.0621200i
$874$			2.14623e9i			3.21471i
$875$	−3.79104e8	+	5.61543e8i	−0.565892	+	0.838221i
$876$	1.72568e8			0.256712
$877$	1.21581e8	+	2.10585e8i	0.180247	+	0.312196i	0.941964	−	0.335713i	$-0.108977\pi$
$877$	1.21581e8	+	2.10585e8i	0.180247	+	0.312196i	−0.761718	+	0.647909i	$0.775644\pi$
$878$	−1.31423e9	−	7.58769e8i	−1.94172	−	1.12105i
$879$	1.34140e8	−	2.32337e8i	0.197511	−	0.342100i
$880$	2.39607e8	−	1.38337e8i	0.351603	−	0.202998i
$881$		−	1.21869e9i		−	1.78224i	−0.453767	−	0.891120i	$-0.649920\pi$
$881$		−	1.21869e9i		−	1.78224i	0.453767	−	0.891120i	$-0.350080\pi$
$882$	3.53176e8	+	4.99339e7i	0.514737	+	0.0727762i
$883$	5.63745e8			0.818842			0.409421	−	0.912346i	$-0.365731\pi$
$883$	5.63745e8			0.818842			0.409421	+	0.912346i	$0.365731\pi$
$884$	−5.53008e7	−	9.57838e7i	−0.0800525	−	0.138655i
$885$	−7.66644e8	−	4.42622e8i	−1.10602	−	0.638563i
$886$	−5.78051e8	+	1.00121e9i	−0.831123	+	1.43955i
$887$	−2.33059e8	+	1.34557e8i	−0.333961	+	0.192812i	−0.657598	−	0.753369i	$-0.728428\pi$
$887$	−2.33059e8	+	1.34557e8i	−0.333961	+	0.192812i	0.323637	+	0.946181i	$0.395094\pi$
$888$		−	8.46038e7i		−	0.120823i
$889$	2.62781e8	+	1.77406e8i	0.374015	+	0.252502i
$890$	−4.54451e8			−0.644639
$891$	−2.58566e7	−	4.47850e7i	−0.0365543	−	0.0633139i
$892$	−1.13698e9	−	6.56434e8i	−1.60198	−	0.924904i
$893$	3.12849e8	−	5.41870e8i	0.439319	−	0.760923i
$894$	−7.79406e8	+	4.49990e8i	−1.09082	+	0.629782i
$895$			8.14860e8i			1.13662i
$896$	−6.16957e7	+	8.77072e8i	−0.0857691	+	1.21930i
$897$	5.46033e7			0.0756557
$898$	1.50201e8	+	2.60155e8i	0.207416	+	0.359255i
$899$	−1.10782e8	−	6.39602e7i	−0.152472	−	0.0880300i
$900$	−2.82661e8	+	4.89583e8i	−0.387738	+	0.671582i
$901$	4.86385e8	−	2.80815e8i	0.664976	−	0.383924i
$902$		−	7.64224e8i		−	1.04136i
$903$	2.65389e8	+	5.44701e8i	0.360429	+	0.739767i
$904$	6.13042e7			0.0829823
$905$	−1.55741e8	−	2.69750e8i	−0.210114	−	0.363929i
$906$	−7.56638e8	−	4.36845e8i	−1.01743	−	0.587412i
$907$	−3.93227e8	+	6.81089e8i	−0.527013	+	0.912814i	0.472491	+	0.881335i	$0.343355\pi$
$907$	−3.93227e8	+	6.81089e8i	−0.527013	+	0.912814i	−0.999504	+	0.0314782i	$0.989979\pi$
$908$	2.40621e8	−	1.38923e8i	0.321423	−	0.185573i
$909$			2.53540e8i			0.337562i
$910$	2.14271e8	−	1.04397e8i	0.284341	−	0.138537i
$911$	1.05328e9			1.39312			0.696559	−	0.717500i	$-0.254713\pi$
$911$	1.05328e9			1.39312			0.696559	+	0.717500i	$0.254713\pi$
$912$	−1.64252e8	−	2.84493e8i	−0.216534	−	0.375048i
$913$	−6.51803e8	−	3.76319e8i	−0.856454	−	0.494474i
$914$	4.05984e8	−	7.03185e8i	0.531705	−	0.920939i
$915$	−2.67552e8	+	1.54471e8i	−0.349257	+	0.201643i
$916$		−	5.73886e8i		−	0.746688i
$917$	3.30934e8	+	2.32788e7i	0.429173	+	0.0301892i
$918$	−2.07327e8			−0.267995
$919$	−5.81563e8	−	1.00730e9i	−0.749290	−	1.29781i	−0.948163	−	0.317784i	$-0.897061\pi$
$919$	−5.81563e8	−	1.00730e9i	−0.749290	−	1.29781i	0.198873	−	0.980025i	$-0.436272\pi$
$920$	−7.70856e8	−	4.45054e8i	−0.989943	−	0.571544i
$921$	−3.20540e8	+	5.55191e8i	−0.410301	+	0.710663i
$922$	1.31845e9	−	7.61209e8i	1.68218	−	0.971206i
$923$		−	9.50875e7i		−	0.120926i
$924$	2.40169e8	−	3.55747e8i	0.304439	−	0.450947i
$925$	−3.99076e8			−0.504232
$926$	−1.64058e8	−	2.84156e8i	−0.206616	−	0.357869i
$927$	−1.64152e8	−	9.47731e7i	−0.206066	−	0.118972i
$928$	1.30121e8	−	2.25376e8i	0.162818	−	0.282009i
$929$	−1.01867e9	+	5.88131e8i	−1.27054	+	0.733545i	−0.975089	−	0.221814i	$-0.928802\pi$
$929$	−1.01867e9	+	5.88131e8i	−1.27054	+	0.733545i	−0.295448	+	0.955359i	$0.595469\pi$
$930$		−	8.04461e8i		−	1.00013i
$931$	−1.25145e9	−	9.79411e8i	−1.55083	−	1.21371i
$932$	−1.08597e9			−1.34143
$933$	8.89276e7	+	1.54027e8i	0.109494	+	0.189650i
$934$	−6.63144e8	−	3.82866e8i	−0.813893	−	0.469901i
$935$	−3.88980e8	+	6.73733e8i	−0.475874	+	0.824239i
$936$	1.99786e7	−	1.15347e7i	0.0243634	−	0.0140662i
$937$			4.63976e8i			0.563997i	0.959415	+	0.281999i	$0.0909974\pi$
$937$			4.63976e8i			0.563997i	−0.959415	+	0.281999i	$0.909003\pi$
$938$	6.19129e8	+	4.17981e8i	0.750192	+	0.506463i
$939$	−1.67436e7			−0.0202233
$940$	4.29911e8	+	7.44627e8i	0.517600	+	0.896510i
$941$	−1.01174e9	−	5.84130e8i	−1.21423	−	0.701036i	−0.250552	−	0.968103i	$-0.580612\pi$
$941$	−1.01174e9	−	5.84130e8i	−1.21423	−	0.701036i	−0.963678	+	0.267067i	$0.913946\pi$
$942$	−4.69210e8	+	8.12695e8i	−0.561325	+	0.972243i
$943$	7.71390e8	−	4.45362e8i	0.919896	−	0.531102i
$944$			4.37528e8i			0.520103i
$945$	1.84616e7	−	2.62452e8i	0.0218763	−	0.310995i
$946$	1.23822e9			1.46259
$947$	−2.84555e8	−	4.92863e8i	−0.335055	−	0.580332i	0.648441	−	0.761265i	$-0.275421\pi$
$947$	−2.84555e8	−	4.92863e8i	−0.335055	−	0.580332i	−0.983495	+	0.180934i	$0.942088\pi$
$948$	9.45262e8	+	5.45747e8i	1.10950	+	0.640570i
$949$	−1.66086e7	+	2.87670e7i	−0.0194328	+	0.0336586i
$950$	3.70415e9	−	2.13859e9i	4.32034	−	2.49435i
$951$			3.08645e8i			0.358853i
$952$	−2.27477e8	−	4.66887e8i	−0.263649	−	0.541129i
$953$	5.61708e8			0.648981			0.324491	−	0.945889i	$-0.394807\pi$
$953$	5.61708e8			0.648981			0.324491	+	0.945889i	$0.394807\pi$
$954$	1.94075e8	+	3.36148e8i	0.223525	+	0.387156i
$955$	7.50098e8	+	4.33069e8i	0.861208	+	0.497219i
$956$	−1.96726e8	+	3.40739e8i	−0.225158	+	0.389985i
$957$	−7.40411e7	+	4.27477e7i	−0.0844768	+	0.0487727i
$958$			2.41132e9i			2.74258i
$959$	−1.44928e9	+	7.06117e8i	−1.64322	+	0.800609i
$960$	1.32141e9			1.49357
$961$	−2.35135e8	−	4.07266e8i	−0.264940	−	0.458889i
$962$	4.67307e7	+	2.69800e7i	0.0524901	+	0.0303052i
$963$	−1.21219e8	+	2.09958e8i	−0.135735	+	0.235100i
$964$	−1.25916e9	+	7.26978e8i	−1.40556	+	0.811503i
$965$			1.30534e9i			1.45259i
$966$	8.47475e8	+	5.96137e7i	0.940146	+	0.0661325i
$967$	6.95843e8			0.769541			0.384771	−	0.923012i	$-0.374281\pi$
$967$	6.95843e8			0.769541			0.384771	+	0.923012i	$0.374281\pi$
$968$	1.73372e8	+	3.00289e8i	0.191140	+	0.331065i
$969$	7.99944e8	+	4.61848e8i	0.879201	+	0.507607i
$970$	−4.29714e8	+	7.44287e8i	−0.470831	+	0.815503i
$971$	−7.65735e8	+	4.42097e8i	−0.836413	+	0.482903i	−0.856043	−	0.516904i	$-0.827084\pi$
$971$	−7.65735e8	+	4.42097e8i	−0.836413	+	0.482903i	0.0196301	+	0.999807i	$0.493751\pi$
$972$		−	8.43757e7i		−	0.0918795i
$973$	−3.15337e8	+	4.67089e8i	−0.342323	+	0.507062i
$974$	1.85119e7			0.0200343
$975$	−5.44090e7	−	9.42392e7i	−0.0587026	−	0.101676i
$976$	1.32236e8	+	7.63466e7i	0.142233	+	0.0821184i
$977$	1.79936e8	−	3.11659e8i	0.192946	−	0.334192i	−0.753279	−	0.657701i	$-0.771529\pi$
$977$	1.79936e8	−	3.11659e8i	0.192946	−	0.334192i	0.946225	+	0.323509i	$0.104863\pi$
$978$	5.71875e8	−	3.30172e8i	0.611343	−	0.352959i
$979$		−	1.57530e8i		−	0.167887i
$980$	2.02543e9	−	8.16379e8i	2.15199	−	0.867388i
$981$	−3.53728e8			−0.374682
$982$	−8.31760e8	−	1.44065e9i	−0.878342	−	1.52133i
$983$	−4.76200e7	−	2.74934e7i	−0.0501336	−	0.0289446i	0.474724	−	0.880135i	$-0.342548\pi$
$983$	−4.76200e7	−	2.74934e7i	−0.0501336	−	0.0289446i	−0.524857	+	0.851190i	$0.675881\pi$
$984$	1.88161e8	−	3.25904e8i	0.197489	−	0.342061i
$985$	4.79128e8	−	2.76625e8i	0.501352	−	0.289456i
$986$			3.42764e8i			0.357573i
$987$	−2.05277e8	−	1.38584e8i	−0.213495	−	0.144133i
$988$	−3.40554e8			−0.353114
$989$	7.21589e8	+	1.24983e9i	0.745935	+	1.29200i
$990$	−4.65627e8	−	2.68830e8i	−0.479880	−	0.277059i
$991$	−1.53556e8	+	2.65967e8i	−0.157778	+	0.273280i	−0.934067	−	0.357098i	$-0.883766\pi$
$991$	−1.53556e8	+	2.65967e8i	−0.157778	+	0.273280i	0.776289	+	0.630377i	$0.217100\pi$
$992$	−7.35101e8	+	4.24411e8i	−0.753029	+	0.434762i
$993$			2.98241e8i			0.304593i
$994$	1.03813e8	−	1.47581e9i	0.105704	−	1.50270i
$995$	−1.20940e8			−0.122773
$996$	−6.14004e8	−	1.06349e9i	−0.621431	−	1.07635i
$997$	1.03839e9	+	5.99516e8i	1.04779	+	0.604945i	0.922031	−	0.387116i	$-0.126529\pi$
$997$	1.03839e9	+	5.99516e8i	1.04779	+	0.604945i	0.125764	+	0.992060i	$0.459862\pi$
$998$	−9.41879e8	+	1.63138e9i	−0.947553	+	1.64121i
$999$	5.15831e7	−	2.97815e7i	0.0517382	−	0.0298711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.f.b.10.1	✓	8
3.2	odd	2		63.7.m.c.10.4		8
4.3	odd	2		336.7.bh.b.241.1		8
7.2	even	3		147.7.f.a.19.1		8
7.3	odd	6		147.7.d.a.97.8		8
7.4	even	3		147.7.d.a.97.7		8
7.5	odd	6	inner	21.7.f.b.19.1	yes	8
7.6	odd	2		147.7.f.a.31.1		8
21.5	even	6		63.7.m.c.19.4		8
21.11	odd	6		441.7.d.d.244.2		8
21.17	even	6		441.7.d.d.244.1		8
28.19	even	6		336.7.bh.b.145.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.b.10.1	✓	8	1.1	even	1	trivial
21.7.f.b.19.1	yes	8	7.5	odd	6	inner
63.7.m.c.10.4		8	3.2	odd	2
63.7.m.c.19.4		8	21.5	even	6
147.7.d.a.97.7		8	7.4	even	3
147.7.d.a.97.8		8	7.3	odd	6
147.7.f.a.19.1		8	7.2	even	3
147.7.f.a.31.1		8	7.6	odd	2
336.7.bh.b.145.1		8	28.19	even	6
336.7.bh.b.241.1		8	4.3	odd	2
441.7.d.d.244.1		8	21.17	even	6
441.7.d.d.244.2		8	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	21.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.23828 - 10.8050i) q^{2} +(13.5000 + 7.79423i) q^{3} +(-45.8323 + 79.3839i) q^{4} +(-175.367 + 101.248i) q^{5} -194.490i q^{6} +(284.280 + 191.921i) q^{7} +345.159 q^{8} +(121.500 + 210.444i) q^{9} +O(q^{10})\)	\(q+(-6.23828 - 10.8050i) q^{2} +(13.5000 + 7.79423i) q^{3} +(-45.8323 + 79.3839i) q^{4} +(-175.367 + 101.248i) q^{5} -194.490i q^{6} +(284.280 + 191.921i) q^{7} +345.159 q^{8} +(121.500 + 210.444i) q^{9} +(2187.98 + 1263.23i) q^{10} +(-437.884 + 758.438i) q^{11} +(-1237.47 + 714.455i) q^{12} -275.049i q^{13} +(300.287 - 4268.91i) q^{14} -3156.61 q^{15} +(780.069 + 1351.12i) q^{16} +(-3799.10 - 2193.41i) q^{17} +(1515.90 - 2625.62i) q^{18} +(-11697.8 + 6753.75i) q^{19} -18561.8i q^{20} +(2341.91 + 4806.68i) q^{21} +10926.6 q^{22} +(6367.61 + 11029.0i) q^{23} +(4659.64 + 2690.25i) q^{24} +(12689.9 - 21979.6i) q^{25} +(-2971.91 + 1715.83i) q^{26} +3788.00i q^{27} +(-28264.6 + 13771.1i) q^{28} +6262.53 q^{29} +(19691.8 + 34107.2i) q^{30} +(-17689.7 - 10213.2i) q^{31} +(20777.7 - 35988.0i) q^{32} +(-11822.9 + 6825.94i) q^{33} +54732.5i q^{34} +(-69285.1 - 4873.70i) q^{35} -22274.5 q^{36} +(-7862.08 - 13617.5i) q^{37} +(145949. + 84263.6i) q^{38} +(2143.79 - 3713.16i) q^{39} +(-60529.5 + 34946.7i) q^{40} -69941.8i q^{41} +(37326.8 - 55289.8i) q^{42} +113322. q^{43} +(-40138.5 - 69521.9i) q^{44} +(-42614.2 - 24603.3i) q^{45} +(79445.9 - 137604. i) q^{46} +(-40116.2 + 23161.1i) q^{47} +24320.1i q^{48} +(43981.8 + 109119. i) q^{49} -316653. q^{50} +(-34191.9 - 59222.2i) q^{51} +(21834.4 + 12606.1i) q^{52} +(-64013.2 + 110874. i) q^{53} +(40929.4 - 23630.6i) q^{54} -177340. i q^{55} +(98121.9 + 66243.2i) q^{56} -210561. q^{57} +(-39067.4 - 67666.8i) q^{58} +(242870. + 140221. i) q^{59} +(144675. - 250584. i) q^{60} +(84759.3 - 48935.8i) q^{61} +254850. i q^{62} +(-5848.55 + 83143.6i) q^{63} -418619. q^{64} +(27848.2 + 48234.5i) q^{65} +(147509. + 85164.3i) q^{66} +(-87278.8 + 151171. i) q^{67} +(348243. - 201058. i) q^{68} +198522. i q^{69} +(379559. + 779030. i) q^{70} +345712. q^{71} +(41936.8 + 72636.7i) q^{72} +(-104589. - 60384.4i) q^{73} +(-98091.8 + 169900. i) q^{74} +(342627. - 197816. i) q^{75} -1.23816e6i q^{76} +(-270042. + 131570. i) q^{77} -53494.3 q^{78} +(-381933. - 661527. i) q^{79} +(-273597. - 157961. i) q^{80} +(-29524.5 + 51137.9i) q^{81} +(-755722. + 436316. i) q^{82} +859402. i q^{83} +(-488908. - 34391.1i) q^{84} +888317. q^{85} +(-706933. - 1.22444e6i) q^{86} +(84544.2 + 48811.6i) q^{87} +(-151140. + 261781. i) q^{88} +(-155778. + 89938.3i) q^{89} +613930. i q^{90} +(52787.6 - 78190.9i) q^{91} -1.16737e6 q^{92} +(-159207. - 275755. i) q^{93} +(500512. + 288971. i) q^{94} +(1.36761e6 - 2.36877e6i) q^{95} +(560997. - 323892. i) q^{96} +340171. i q^{97} +(904659. - 1.15594e6i) q^{98} -212812. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} - 42 q^{5} + 748 q^{7} - 454 q^{8} + 972 q^{9}+O(q^{10}) \) 8 * q - 5 * q^2 + 108 * q^3 - 173 * q^4 - 42 * q^5 + 748 * q^7 - 454 * q^8 + 972 * q^9	\( 8 q - 5 q^{2} + 108 q^{3} - 173 q^{4} - 42 q^{5} + 748 q^{7} - 454 q^{8} + 972 q^{9} + 261 q^{10} - 1070 q^{11} - 4671 q^{12} + 6070 q^{14} - 756 q^{15} + 3911 q^{16} + 7212 q^{17} + 1215 q^{18} - 24606 q^{19} + 8154 q^{21} - 78 q^{22} - 15224 q^{23} - 6129 q^{24} + 22274 q^{25} - 19044 q^{26} - 3415 q^{28} + 32524 q^{29} + 2349 q^{30} + 40200 q^{31} + 70203 q^{32} - 28890 q^{33} - 242436 q^{35} - 84078 q^{36} - 45670 q^{37} + 503310 q^{38} + 93366 q^{39} - 94941 q^{40} + 55161 q^{42} - 445660 q^{43} - 188829 q^{44} - 10206 q^{45} + 525804 q^{46} + 82884 q^{47} + 24116 q^{49} - 1218884 q^{50} + 64908 q^{51} + 722856 q^{52} - 13034 q^{53} + 32805 q^{54} + 127061 q^{56} - 442908 q^{57} - 159501 q^{58} + 1810362 q^{59} + 429705 q^{60} - 392856 q^{61} + 38394 q^{63} - 1410446 q^{64} - 389004 q^{65} - 1053 q^{66} + 384094 q^{67} - 1616346 q^{68} + 406005 q^{70} + 225688 q^{71} - 55161 q^{72} + 903078 q^{73} + 1185530 q^{74} + 601398 q^{75} - 327674 q^{77} - 342792 q^{78} - 559592 q^{79} + 847713 q^{80} - 236196 q^{81} + 347634 q^{82} - 879444 q^{84} + 1953576 q^{85} - 2302402 q^{86} + 439074 q^{87} + 304887 q^{88} - 1770036 q^{89} - 2960718 q^{91} - 113064 q^{92} + 361800 q^{93} - 1837620 q^{94} + 1160112 q^{95} + 1895481 q^{96} + 5732467 q^{98} - 520020 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 + 108 * q^3 - 173 * q^4 - 42 * q^5 + 748 * q^7 - 454 * q^8 + 972 * q^9 + 261 * q^10 - 1070 * q^11 - 4671 * q^12 + 6070 * q^14 - 756 * q^15 + 3911 * q^16 + 7212 * q^17 + 1215 * q^18 - 24606 * q^19 + 8154 * q^21 - 78 * q^22 - 15224 * q^23 - 6129 * q^24 + 22274 * q^25 - 19044 * q^26 - 3415 * q^28 + 32524 * q^29 + 2349 * q^30 + 40200 * q^31 + 70203 * q^32 - 28890 * q^33 - 242436 * q^35 - 84078 * q^36 - 45670 * q^37 + 503310 * q^38 + 93366 * q^39 - 94941 * q^40 + 55161 * q^42 - 445660 * q^43 - 188829 * q^44 - 10206 * q^45 + 525804 * q^46 + 82884 * q^47 + 24116 * q^49 - 1218884 * q^50 + 64908 * q^51 + 722856 * q^52 - 13034 * q^53 + 32805 * q^54 + 127061 * q^56 - 442908 * q^57 - 159501 * q^58 + 1810362 * q^59 + 429705 * q^60 - 392856 * q^61 + 38394 * q^63 - 1410446 * q^64 - 389004 * q^65 - 1053 * q^66 + 384094 * q^67 - 1616346 * q^68 + 406005 * q^70 + 225688 * q^71 - 55161 * q^72 + 903078 * q^73 + 1185530 * q^74 + 601398 * q^75 - 327674 * q^77 - 342792 * q^78 - 559592 * q^79 + 847713 * q^80 - 236196 * q^81 + 347634 * q^82 - 879444 * q^84 + 1953576 * q^85 - 2302402 * q^86 + 439074 * q^87 + 304887 * q^88 - 1770036 * q^89 - 2960718 * q^91 - 113064 * q^92 + 361800 * q^93 - 1837620 * q^94 + 1160112 * q^95 + 1895481 * q^96 + 5732467 * q^98 - 520020 * q^99

Introduction

L-functions

Modular forms

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